Best Known (100, ∞, s)-Nets in Base 27
(100, ∞, 324)-Net over F27 — Constructive and digital
Digital (100, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (100, 323)-sequence over F27, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- F4 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
(100, ∞, 325)-Net over F27 — Digital
Digital (100, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (100, 324)-sequence over F27, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 48 and N(F) ≥ 325, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
(100, ∞, 2662)-Net in Base 27 — Upper bound on s
There is no (100, m, 2663)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (100, 5323, 2663)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(275323, 2663, S27, 2, 5223), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 392 209046 937528 693561 612989 765562 228493 099315 961530 668275 668091 196734 500719 353748 802975 975432 854470 159314 846067 916077 374046 972237 612658 333937 624533 458892 852217 979866 699010 315521 474298 299038 628621 816406 039362 443247 896175 294792 849896 520232 150170 178031 962417 841898 465532 977910 265297 803581 115371 396675 768139 908648 842263 451300 978296 000650 287283 706337 736298 894648 424720 613608 319079 875331 627756 007527 067469 794028 165092 610607 872096 240578 053139 623274 470840 496371 829429 810732 655746 529774 750912 633559 161555 010467 162039 995004 280641 665707 476662 912414 178977 440793 709527 220986 208760 977577 417606 965791 726163 404956 992301 455444 000321 668562 806775 757728 039562 235012 468636 704864 729503 404810 980748 667333 623333 321557 960001 245096 700516 553730 092982 273071 594575 944067 147192 015118 509023 676906 448056 082221 660533 885982 399098 365938 561947 686867 615503 256345 329991 999725 533907 950857 996857 943764 233134 565018 548417 674721 115264 408405 391403 393505 629767 971836 222469 934904 549793 450891 322462 476145 212070 882844 479782 288800 481555 911674 196202 634416 000493 601611 968818 279635 048637 777786 563330 667743 784729 727678 011457 548007 355476 491065 882270 279489 617810 455853 451645 561952 984998 074558 295506 756461 790912 269359 174989 482815 302307 535425 212178 635501 237872 823214 618703 893859 546671 101612 834760 420173 366321 042179 534065 801508 796672 615080 621076 268176 131822 719826 378199 496187 894945 685252 828638 318301 129973 601260 572293 334170 865808 198294 951471 698845 838838 056976 035291 519667 615046 653332 900704 000041 994335 691917 696070 223254 154820 456983 778970 733491 203992 236921 980127 315167 936948 843250 029219 418554 840469 913714 105020 728690 309477 869318 445848 879792 057484 445335 594678 296679 546408 957725 530466 955110 856096 465973 922201 563390 820353 467590 555622 392024 797742 644935 926063 008836 695219 494012 797114 580754 112952 838583 798440 031057 546438 758717 515715 620420 248273 363683 726152 011627 779581 067638 815734 457054 993686 635681 260360 743660 348178 324693 423628 986720 038420 468510 815721 310990 957654 118748 645555 405478 410634 968281 149954 683725 137245 984493 547482 371704 013633 526414 469511 810157 932947 430870 227288 444075 216382 733355 252171 335977 096386 161618 525692 770432 681001 377227 524567 931676 405309 957698 511434 158528 386485 409395 879549 812221 569872 994189 716663 891422 301145 487579 471774 797461 840446 606351 321668 411630 906917 621224 600610 114780 484989 385373 661724 579295 205218 678643 970364 711909 601634 220554 828405 132785 246047 760240 469576 501489 546506 712612 578108 697245 495453 046415 236524 004255 590557 437611 256256 396017 212030 569559 738108 776393 571599 767828 395972 513777 894486 601432 230490 375084 653992 534174 341710 342580 197109 286826 088263 282003 575066 023826 590546 320218 318858 714959 270442 073423 720874 324366 742482 889579 533899 085891 409375 454732 313502 879080 689321 866252 295333 884126 663700 822659 744147 235256 677230 565578 476506 351124 549456 098253 668838 017312 254981 376516 495221 855653 124556 694564 957682 895672 410316 724605 939435 083689 733540 763513 300808 395322 355708 821951 999196 305669 076809 374713 557767 368249 552458 117261 111572 866431 844572 180171 917440 952473 088248 277174 694475 696531 000211 577520 844621 600943 594371 597829 596273 249572 037851 321412 406559 702632 040865 058827 958917 224952 337308 173993 432750 755233 530738 419212 099445 647288 778430 998656 083595 682934 644442 314793 293510 539720 759223 263056 690045 493613 861158 637611 689966 657726 473302 298937 446677 943198 409623 781190 235273 291971 818591 507597 755517 503640 518820 791764 870073 114449 275368 911088 782921 601996 292293 699593 181761 623306 239569 618049 377174 187798 417246 407719 934015 896395 900493 307679 538740 864475 597196 792707 282774 594956 329399 007703 360008 151695 158934 837299 969729 960243 690488 007820 895717 409163 485133 591712 848584 826978 324860 094604 635613 266946 884730 278728 079444 956982 117328 752860 775780 048854 863169 630983 314465 008801 887523 602852 586607 722923 465003 239340 223820 472568 535817 206138 986782 790553 948364 627088 759948 037097 580251 775224 505477 722225 711611 010299 927953 519842 945971 175462 368077 861528 957043 783948 536104 079360 359157 714577 746409 149599 801794 987560 991238 667879 812783 932734 001726 132894 608798 383532 926898 778808 281834 727642 603615 718161 665912 036101 348008 838922 127543 951246 774247 359686 094755 526910 639350 996074 810347 818984 899683 631785 770280 125381 385693 662898 301766 965539 999713 739500 913333 045517 554743 769291 079591 846665 474526 169678 145693 968759 865139 289029 124634 669735 552501 878695 389594 009574 783242 015914 936696 205188 520650 335559 913147 575153 473714 474647 248758 560927 304472 546194 790459 178072 885950 473938 190718 778866 132659 436600 085707 431536 947115 236221 701874 972881 020291 751791 174773 417944 665047 951664 499512 520278 358007 971505 914700 523297 467655 342166 548262 351877 973385 006397 221046 814910 810388 321431 016864 736035 676282 263507 522288 336409 626109 812883 299244 437798 003490 189268 456464 563698 701011 432470 042789 570488 621550 414435 354986 064696 482371 875290 895251 214152 207933 185605 612190 049654 061376 676270 712737 095436 908493 984345 944601 600582 902297 034368 134932 864324 415423 759846 287936 307329 802167 808528 653748 398899 407534 008668 328282 294161 240713 853919 408496 748111 726958 938189 289428 516363 199335 504184 949020 415128 989764 794997 150744 771322 777427 534197 220968 780309 059432 013702 819444 753262 436040 566901 344636 148465 375528 264270 822169 202972 716623 614967 326298 676938 975788 766656 053907 108370 218995 765375 665037 324248 516957 954459 193061 029378 346830 989545 790959 844898 876046 725534 496692 090564 111707 173527 314782 332034 995380 043797 674468 068155 485762 091573 079548 748322 258382 715967 557214 332214 012223 987229 235316 334379 728243 050993 092051 533321 645848 848943 318112 377991 167951 852883 808165 598863 606785 629824 093444 243219 512199 315603 834438 688051 866565 957458 174139 471848 921103 330332 173126 412207 292038 018845 568785 420521 465985 156097 349683 441669 009289 253629 020063 052172 766253 998662 355000 959565 700834 083642 048060 494869 935208 352682 222217 719187 379724 759463 895109 197833 771256 341979 537083 889551 766300 911346 562905 361068 985900 825717 755432 423618 128689 264501 898298 054199 257362 621844 082508 582067 104938 139623 505629 123317 669011 474098 653466 009216 552755 333162 713223 458821 308865 707701 520299 935978 202258 760253 154358 208660 277880 359137 310639 068202 952590 042804 982360 051509 119968 076040 496967 969113 325336 328247 187989 514298 143516 222767 583536 793160 381510 444378 715861 347613 102614 196583 162101 664524 426466 417079 943575 428680 084177 021123 135290 557362 988390 957856 362284 770965 868350 413741 840402 843453 235578 590501 039704 352899 922692 841625 814810 766046 185494 277069 488049 687700 142515 031650 438368 284964 891733 648854 058441 940500 953189 709585 276694 562440 988571 008073 111817 907290 156468 872825 555355 228039 656371 718638 620875 382847 675469 489408 938492 364592 259987 680260 260973 372478 582890 427295 913936 323668 270008 510201 335729 352149 421725 798530 075630 927380 107184 035969 999953 650860 273556 106691 121976 351509 630348 615620 097303 750287 413187 319383 107695 140281 393489 073164 728033 167787 536392 051927 212239 139059 584369 855811 517785 916612 983866 951866 425231 333385 900451 699218 727584 085003 444749 738776 833720 560084 102752 503863 487422 374989 365080 394145 742290 843544 434802 234098 541465 693174 829854 114215 763873 797592 115370 066985 401459 028738 948557 497172 732339 930248 284790 930624 650863 393943 137526 933064 998651 556083 689903 333993 020479 357674 547681 539946 270616 333125 200163 158047 581432 981128 576537 996620 740172 917493 770427 212316 916304 322006 715034 749449 669394 012321 785457 995642 895213 292535 424078 219499 313367 435936 957928 901675 891820 340599 254963 858061 228398 532349 820142 330575 531301 832745 749035 293453 760264 222987 487985 015069 396617 576341 676453 982308 444556 904765 018763 558751 729824 099670 986323 478906 071531 477655 168643 987920 230498 408460 322474 880215 127165 873577 263350 201614 540268 169151 851096 980459 850081 707395 503039 661654 244525 618178 027451 152237 900459 319667 950338 751939 853464 299156 261053 047467 388112 634054 024706 316000 241463 832963 291036 673952 043073 923374 610581 080211 466807 931771 094945 748233 406983 429139 715570 557801 653389 239440 295142 091207 422538 116151 564033 165733 179822 810792 263832 780197 536023 / 2612 > 275323 [i]
- extracting embedded OOA [i] would yield OOA(275323, 2663, S27, 2, 5223), but