Best Known (90, ∞, s)-Nets in Base 9
(90, ∞, 222)-Net over F9 — Constructive and digital
Digital (90, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (90, 221)-sequence over F9, using
- t-expansion [i] based on digital (79, 221)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 222, using
- F4 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 222, using
- t-expansion [i] based on digital (79, 221)-sequence over F9, using
(90, ∞, 245)-Net over F9 — Digital
Digital (90, m, 245)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (90, 244)-sequence over F9, using
- t-expansion [i] based on digital (81, 244)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 81 and N(F) ≥ 245, using
- t-expansion [i] based on digital (81, 244)-sequence over F9, using
(90, ∞, 747)-Net in Base 9 — Upper bound on s
There is no (90, m, 748)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (90, 2240, 748)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92240, 748, S9, 3, 2150), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 8633 570405 418104 664613 431003 797227 620408 193706 646407 094244 476683 238567 909206 210255 409983 448444 092878 498066 532341 425414 079035 895954 328314 137156 128514 964034 329984 711578 155584 140435 158085 202101 205727 308291 508321 058053 527457 793725 450989 271470 229923 844101 677596 847292 424332 159499 609519 577212 719757 369182 757805 677475 874533 294123 663016 862986 729161 860031 136281 719345 585258 073787 793726 906617 441588 128665 187348 699887 788610 553496 124826 165176 487332 880021 931212 774259 131784 429929 469209 887502 830560 444604 655661 766730 611155 263762 770697 581914 877851 379822 730943 527861 301837 418232 787360 737394 396768 920107 001200 179481 786896 496555 748513 860687 592491 958489 510869 039791 914989 058927 345701 891601 666264 444852 903297 776043 973385 302350 890790 545558 030070 960253 276462 257211 343113 431792 720090 590076 603735 944447 010837 692258 471298 259034 575237 747998 998882 002121 660833 847359 900308 651223 611522 273643 862810 991953 689417 215837 563288 865227 001757 738715 121584 453378 252917 597278 341198 075184 971043 097268 252634 866928 872064 289278 232752 351903 148529 861207 123543 058281 574083 240318 805527 802618 304038 462317 578967 599612 367995 161558 603636 566760 812486 677700 367807 673878 915908 531653 191332 136498 816021 956215 869379 027831 968647 955449 695282 401483 259093 313258 198505 376874 471513 767680 369093 934107 090029 183033 721565 848646 596741 096728 178499 307458 837903 959628 423495 218373 657616 767277 621820 513291 800444 057214 574496 526040 899597 790536 653766 539123 403443 964564 906068 306843 460215 060011 508052 968201 940024 610148 902128 816669 161583 231878 941541 913608 763507 192656 701280 672223 368274 252694 691911 469264 733013 099229 162906 574111 189754 766402 480579 039087 241012 189400 694922 995276 344956 267118 756749 443853 028886 652999 446689 423642 515934 994721 215865 296370 005195 711015 009366 697320 370111 128683 715355 835514 368030 954074 527789 937507 471601 997843 198103 340095 510682 526525 568218 446462 970290 471237 859131 064939 389353 793291 991454 166160 554297 876713 092917 076009 901618 266017 466020 490325 548984 499231 162670 219516 792626 481569 048594 220062 358696 588999 362217 425993 510060 063030 080002 349004 089645 380436 838419 010379 791177 158991 350919 128408 782489 497386 495121 058989 381896 241661 741406 077308 255550 608290 650579 801488 367166 734205 975740 229850 062873 728322 777871 / 239 > 92240 [i]
- extracting embedded OOA [i] would yield OOA(92240, 748, S9, 3, 2150), but