Best Known (84, 84+∞, s)-Nets in Base 27
(84, 84+∞, 324)-Net over F27 — Constructive and digital
Digital (84, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (84, 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
(84, 84+∞, 325)-Net over F27 — Digital
Digital (84, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (84, 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
(84, 84+∞, 2244)-Net in Base 27 — Upper bound on s
There is no (84, m, 2245)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (84, 4487, 2245)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(274487, 2245, S27, 2, 4403), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 252656 446210 510621 977204 952833 853630 313349 869751 232776 869540 673276 684915 946868 639183 613048 797225 742694 061104 778628 726915 640426 705870 998387 649502 277926 505594 339015 643863 063285 169299 710895 791718 789518 323883 718004 037088 346939 587722 103333 549140 591047 670865 826270 242062 543059 414019 950853 013098 616083 661147 348579 599824 540466 348547 055988 283582 403455 579623 691240 148140 700975 550093 360150 451831 590590 231763 183987 674965 598720 425848 537413 609498 860942 711890 380930 364347 035575 699577 889723 568378 125820 722312 139792 050980 676431 834554 644557 212950 648286 920426 788577 464789 812731 570953 550378 784011 830764 870011 251631 723534 062035 720947 495774 896475 925576 787644 231537 182989 297777 046812 641549 194303 284096 841380 835437 982302 337154 066057 006557 621856 157262 364958 089912 061278 242411 535032 964171 225807 582410 164689 072603 982261 045165 939728 304372 312936 295912 364964 724771 320657 466263 098025 382512 756706 401369 570002 306575 104970 110294 813737 801302 976844 746333 497556 615003 130841 615037 415020 698133 839284 482783 871932 264136 244524 596997 102667 557582 871072 517599 507073 938717 945693 731399 753837 134500 970863 195830 943963 601913 631000 617809 346067 582409 444222 555468 002473 432353 739817 225210 145759 763227 948240 639806 164046 642995 737315 102258 921145 990086 940881 541160 480172 606320 136012 841504 650071 177474 724212 819575 328130 767565 989533 520785 482240 054964 328369 178186 125484 568008 233890 342354 238764 610934 426863 858266 839473 191047 462276 145148 417049 603515 651460 115024 322015 654260 490147 738473 937568 001651 926661 118532 578210 340704 653056 028438 451998 525733 785796 260458 342653 913231 469658 886180 442433 668293 925846 658546 792452 620064 246844 326649 779380 710337 395838 052812 201346 950044 258796 839955 550609 354446 996925 201532 212823 637778 811222 602454 360827 589106 444466 663984 387676 295436 877737 309564 820949 659414 038651 169314 835390 422363 256618 615929 019357 548856 849198 985183 924178 411585 541785 251603 899714 892115 649620 881447 032885 748056 523070 353221 525422 765849 736409 164395 525886 003222 407440 817541 525645 418383 814589 970479 541741 707800 166591 952370 872151 878348 586201 674904 145115 397519 049369 931255 923514 143638 095172 898993 320010 849927 831287 140388 401982 436129 146261 778596 891923 366519 228246 162199 150034 996856 196457 691476 170775 349442 602336 536215 033142 017129 493285 929600 043345 308532 049494 196559 060351 403095 381313 240105 312160 764338 566219 131089 169515 870181 149319 566604 147592 661967 157788 035926 876059 516364 370528 191515 068763 521071 344653 834844 380469 777602 630539 128822 807488 235819 651017 713349 983271 653742 817396 237523 041901 457688 919881 018031 147083 897997 216116 582741 034267 525128 295360 018964 025360 493210 788557 709005 464053 339344 977607 125006 450537 447545 302552 682700 949767 910983 374570 821271 275859 928082 593945 714434 467578 369140 597238 097934 249614 851112 166298 013246 592755 231517 380895 249141 693577 947592 880650 215683 727190 143303 233111 206323 165890 550867 482837 567299 492487 639160 392585 291384 410083 594486 529771 196820 137665 021339 216971 911956 332772 816322 230023 271808 895461 741124 411459 131010 111407 455660 593748 187646 431339 090983 250848 170571 241000 310159 999050 908183 526887 808616 806435 657452 215636 881204 194820 932800 978890 698466 498193 226978 811336 296639 057097 327601 380836 081087 545583 814983 336818 107579 147574 500540 982185 046237 680698 161339 078045 962199 719151 445457 098258 777421 240524 197307 281530 378962 770554 150624 382991 084158 087696 425614 204907 259023 718025 235111 201205 465306 763303 203895 539007 953857 231237 502829 411911 134688 533348 251328 212961 986505 910249 766083 747371 551057 411219 795766 040140 521827 108496 567359 078350 554140 409869 840952 029288 808847 913270 240177 741322 943744 061690 867681 972123 147245 357778 181785 315364 780543 193962 569038 609741 838832 512594 205848 829551 721011 611633 832756 375874 261730 221548 288771 828741 751749 125764 755228 731087 316332 988352 835568 220758 965837 960775 822179 559478 208137 864696 565154 957088 582906 918943 406176 834657 215404 856591 354218 780242 483054 668932 751191 410987 686652 755871 549281 631139 765728 770043 307946 430853 357909 274034 636991 793670 277705 338104 373274 444917 999006 999935 840049 000375 167649 143405 548467 143743 193200 304814 263385 049112 900533 296884 695573 587617 959767 306752 935493 309662 543947 885676 623778 214800 368143 769584 896042 995439 647263 085835 676980 007677 507783 658648 031327 941001 989214 939073 956001 546139 774508 395089 793166 754585 746895 677788 692704 269259 074491 786411 659760 588318 392132 355754 656914 228470 206326 550055 641037 412803 065909 500748 625405 314426 046294 238373 250787 855589 490770 669160 656695 572708 590501 465862 222529 024969 697157 831000 341742 921575 617049 357535 284275 997618 164435 613995 338448 374212 609681 042715 937349 279347 509704 945616 254441 532388 253004 431664 482463 184137 987999 283901 101302 632153 415556 254356 810609 323164 585043 794949 872432 604674 285433 199004 283414 782810 739460 011111 113128 395530 846444 528624 072092 898118 904448 376266 451654 070575 913395 072427 528275 865459 134478 878905 613838 148961 115749 009356 186820 795186 681773 755445 571313 235043 358532 254938 233479 511352 906605 390495 407001 505090 999853 956670 978079 561475 619299 997266 280471 631202 879430 656276 918604 363788 953887 665553 245070 749245 165471 968237 833937 284523 545001 756941 183029 014431 764834 310295 333122 026809 858522 716874 339232 886836 516749 618758 393860 746696 553519 135539 736331 278207 831194 402687 040989 066936 502348 434324 607533 627046 800028 386759 233863 400821 174928 601034 941176 826870 387547 856295 247212 360642 038093 460646 118102 089411 579115 970269 957872 704859 795358 648201 744989 928832 622987 721553 067029 354200 684350 068618 395300 520952 315356 656769 551233 564057 810777 822930 689823 249666 721278 206978 926674 875975 947520 674966 385103 286460 125010 007810 594184 615376 089884 149358 116045 254356 552495 000178 020102 628529 458671 654409 778438 226942 449816 439732 590920 968315 892360 008278 084923 229270 121291 640757 318736 245309 993438 192059 793931 947346 968943 220667 794413 501782 935013 954497 984371 273831 143920 605837 702615 194516 700793 110002 933339 688683 166330 987600 007956 653341 095276 802929 417729 278419 827043 469214 887478 110229 887104 287974 958730 250428 823925 728332 804745 099470 911685 069019 980395 025719 090207 065543 506170 958221 706159 514784 625731 236474 752128 630224 482417 725734 895559 073362 258179 465002 442250 849841 649650 527858 056742 995961 524694 808841 147874 475398 935478 665735 843040 825356 173400 212485 338722 731222 875226 320622 357395 285519 233958 083251 378245 656592 254147 310348 995086 190191 643411 278518 516778 266898 438358 537113 548180 914496 827683 099887 714682 343076 271329 274433 537025 909998 343880 035412 366582 863513 973764 221234 491687 470334 192452 170769 381557 508810 457488 535540 529326 974695 029353 971086 418841 734833 859488 814696 454603 059981 539533 187578 946435 753009 296862 981050 109795 665958 401234 011936 455030 650770 036381 148848 915625 778339 785519 846714 774699 247453 033501 194587 189141 892490 489493 073457 871441 / 734 > 274487 [i]
- extracting embedded OOA [i] would yield OOA(274487, 2245, S27, 2, 4403), but