Best Known (86, ∞, s)-Nets in Base 27
(86, ∞, 324)-Net over F27 — Constructive and digital
Digital (86, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (86, 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
(86, ∞, 325)-Net over F27 — Digital
Digital (86, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (86, 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
(86, ∞, 2297)-Net in Base 27 — Upper bound on s
There is no (86, m, 2298)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (86, 4593, 2298)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(274593, 2298, S27, 2, 4507), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 23 247367 642619 146644 039707 971367 792467 595913 013578 788846 410695 575043 303246 732842 746242 693320 466317 473768 017061 226379 673085 047235 041321 646289 868351 680269 699541 927330 298020 834333 266292 989420 313743 472856 921059 415167 727111 991108 648536 284498 129170 819402 657759 770051 924748 244608 718792 345906 992104 719539 832559 803578 489744 808359 797910 666698 742525 206263 324434 301222 111056 825501 768724 217594 392512 648101 050745 423027 055769 843500 606248 146929 073911 287913 092864 746930 273943 535721 828223 921986 463582 753525 127602 383061 978143 871516 604292 583151 170450 612932 460784 243864 123478 055976 666138 757279 082861 065065 106461 816853 555501 834371 704706 488376 924426 419188 641968 249421 041761 731811 604950 459369 902616 305019 255239 181441 524925 850846 113870 440965 839407 109597 408438 988556 083234 821388 641783 331427 124539 687559 613416 669359 059653 272049 767571 209915 421827 919268 236334 768274 991793 814629 975186 503300 832703 025192 581154 774302 946354 715515 965216 280324 561664 889744 643347 513689 716102 792963 145747 625694 684609 778622 334918 816504 000860 742865 432567 133480 817731 617050 200868 207863 114902 759705 167556 729002 918767 880123 296369 119338 227844 583457 905587 598016 419750 367076 541020 100013 190902 130201 413260 751868 579655 700326 847161 666507 389235 985573 859897 489906 865426 983753 828554 085433 300587 545125 855993 804934 190172 052803 504155 440327 750591 819646 825868 650539 262720 128958 021382 503510 843580 912778 441133 139874 899815 405505 150982 320092 879680 961633 523653 504286 350719 193039 783301 707479 328375 866699 969478 683839 565011 960223 241404 187878 478931 764250 976307 101097 414588 769764 474102 718427 262480 487609 565679 855556 638197 677591 308781 254540 068754 260535 096709 001375 369685 313512 791639 863617 098866 599452 813404 162467 953623 183522 794474 552052 521341 185255 000133 536545 781644 984418 359515 772237 206968 643122 866397 709860 380186 858582 061524 768867 562774 824969 525793 982551 406311 006053 923761 806849 836735 602406 229855 402361 858664 788859 535133 293140 853260 977096 718765 287424 516430 271033 150325 308942 240034 554691 208853 452243 256924 038840 003857 016048 794991 689359 928589 373176 822923 166972 936837 259176 141149 409560 519131 337018 558105 313266 746831 973065 317178 714507 597058 259404 312543 673163 158587 581757 143316 331911 633400 027714 224698 086856 854884 526638 584702 225780 798852 130824 459609 095405 513358 760042 365520 201139 382559 764467 723244 004479 865108 130419 214625 770333 160737 800525 423467 147950 080739 326743 929183 420435 605581 866421 987275 403092 801493 326840 229376 079851 914515 929121 188456 416260 094591 914330 052031 824591 609305 720453 228287 959020 991788 624180 153143 592351 170234 804375 189666 039153 884299 571682 821762 127923 590280 463526 818667 730569 761102 781135 921256 945108 165316 580473 952491 538043 193457 913968 878771 981483 579519 942201 099840 845857 330591 188677 518991 136910 464147 103472 155304 346892 444651 301154 567292 338735 043481 708167 119535 201385 894544 390560 171962 511620 166385 356590 886035 947597 666571 959122 102759 562313 376519 277207 242963 011404 565475 340269 159951 545259 881803 159202 531314 942380 551223 390288 904242 373328 715644 265667 735156 957017 732969 495639 112700 453152 599780 558367 580258 512282 829023 270293 868794 348531 066413 300328 684782 670582 935685 945170 909880 833995 188994 436941 766626 292244 069203 616063 532532 038808 662898 235059 955753 448812 898904 782648 892071 954419 540200 549919 741954 959791 566869 878922 431791 938595 799858 370633 773737 517176 556281 963609 939354 190181 550080 128325 886952 723520 998624 574553 549390 922695 867405 353323 250212 412545 760389 215832 917658 368880 926496 027952 617069 601877 236796 719795 939436 622851 712699 257844 250405 882681 008982 619810 651963 448762 289466 354066 974362 229369 359752 498198 310927 487163 722547 611179 300915 430003 266402 032338 425886 621624 920066 303303 316889 444561 102235 130866 537511 343103 527790 805281 149476 150830 073190 474678 195203 424598 916656 187525 748535 017322 828048 763978 886199 701634 027425 568489 491835 189657 436180 580352 066666 824982 972984 269653 305292 371251 452884 509572 798191 400694 425340 510442 018285 889943 832539 680948 937688 766142 423540 101253 687094 846737 008344 208594 833490 592024 749239 916957 621719 413190 740149 468540 338153 399914 377189 250921 644088 287879 220445 466619 803843 248173 936578 517201 151868 361826 454030 363169 888611 878793 048793 797609 080452 659488 212322 029865 587586 670149 406464 159322 064254 390712 687779 899905 181504 180398 194361 010622 932630 692008 778863 672984 751800 712807 545153 065789 344381 261914 868038 115004 505897 469626 370677 559428 475299 198960 798512 715067 631928 981411 805469 872903 001200 668141 018750 882144 412739 912585 251758 206048 849930 342648 910789 533823 344266 131086 106492 355653 805535 317487 692276 776945 433327 898000 481449 998700 256591 005591 978149 388307 360134 574480 624219 482849 026760 665999 390956 626808 671717 164082 299570 841601 025845 079517 387097 908860 036188 465541 986163 545386 148077 289666 414042 080931 196423 121540 072511 598598 378124 591980 357436 213895 987702 302722 981310 753697 109766 360494 024958 335992 561701 123225 650353 429603 653881 742870 473514 885275 560756 076054 529599 149155 742181 362948 865958 045151 037791 913526 881625 271486 327404 847893 866263 397725 348303 283194 718748 602925 762978 464009 592927 416756 290278 996726 281251 364943 949494 454239 639328 819122 135563 937707 790230 121326 507699 963987 860821 012919 126163 591411 944782 646886 063503 337657 084862 377077 618042 117916 948789 360764 459299 245838 690820 648183 909670 671013 236604 277719 046876 465202 263619 347249 461681 070853 439693 435431 364011 435483 905002 328234 910859 482498 974178 652062 006148 435925 170943 938926 376912 273144 671508 915743 537320 445689 792699 526007 410913 031850 144821 628237 319311 762491 106387 710661 871842 106310 264361 144483 680859 815109 879505 209390 438168 373529 549220 677472 107141 394723 953016 540442 511011 423070 791176 221790 529954 128802 348842 290494 385416 639665 784168 765538 300251 853648 826372 299156 145132 686700 090342 040000 092548 885530 989615 469277 283779 309646 169401 165791 018464 757971 486603 461453 226943 209895 426097 082255 033033 473765 268510 985451 143254 234309 311764 072872 691926 674299 651827 624066 624470 224241 775247 438457 803275 823359 492566 837479 927118 020156 531806 278897 425472 092129 886940 408496 739165 078376 769294 665860 472513 889280 285044 101686 737113 101186 644083 417241 017571 303836 979688 184965 253492 739831 600058 674565 395260 243883 068146 139578 498958 020724 777628 466757 942340 593533 806516 978356 373151 682554 681260 653662 858620 288799 380674 548333 311746 165808 841869 856820 265103 221607 065250 648544 023153 417794 421223 768319 768374 325824 279532 788384 475815 137808 593341 156196 541922 072791 812680 364149 395881 398966 549281 552073 131686 168670 103169 784498 195127 862103 206555 171508 560851 525816 476521 345044 352067 581425 482758 145141 436593 687995 021676 334514 617208 391524 103824 414329 432353 002863 440911 014843 314983 501680 592202 896587 139226 115034 275893 452445 282692 451101 832551 408140 185006 188765 369529 104100 320134 226438 451771 615239 656227 769254 181462 047074 269654 863412 970737 232406 564295 637800 459237 001659 589839 745704 290502 814791 150691 289542 028826 832729 696330 009062 465478 695259 411632 / 1127 > 274593 [i]
- extracting embedded OOA [i] would yield OOA(274593, 2298, S27, 2, 4507), but