Best Known (81, ∞, s)-Nets in Base 9
(81, ∞, 222)-Net over F9 — Constructive and digital
Digital (81, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (81, 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
(81, ∞, 245)-Net over F9 — Digital
Digital (81, m, 245)-net over F9 for arbitrarily large m, using
- net from sequence [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
(81, ∞, 675)-Net in Base 9 — Upper bound on s
There is no (81, m, 676)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (81, 2024, 676)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92024, 676, S9, 3, 1943), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 315895 460761 566528 732050 920641 693954 104525 314791 372711 570165 662270 919918 559786 283136 434228 896281 139874 166125 724458 422789 262200 910956 763318 525099 532307 009355 639567 889879 636352 353094 911101 626377 023554 154980 392719 452990 253887 539720 140942 777322 697624 493050 042852 301524 358062 431196 738934 767348 640533 224204 963537 036989 479810 994485 781911 914070 909485 841208 703792 699801 048230 373378 502654 768875 240696 862011 895131 362560 331291 865676 925532 047376 722812 017564 459950 980366 647241 777590 739106 512221 054544 433314 466248 148682 224497 142692 329409 007608 485311 898775 945402 511517 879754 156400 259433 239486 591923 719727 695524 153074 799158 275350 411766 961120 602746 570259 938407 853656 874940 343235 444151 818655 978412 873558 411642 192574 580220 076400 792884 145870 275834 835916 596643 842166 965485 414379 726152 876466 245369 445522 345809 560267 112904 912456 130501 674114 837502 013528 299591 715386 350718 627109 031045 730960 513777 227939 119519 231172 368951 893378 521370 543445 691274 904789 940023 692835 454433 904514 927130 160647 831660 563547 344947 252501 519286 466798 194438 086546 699531 677339 325264 347667 993646 374091 012920 216166 844117 432238 196372 951089 178328 958512 056522 392166 221559 644232 491235 106385 014809 478519 028063 169938 488358 756973 670280 643682 792504 118179 194293 544370 969734 160700 458011 084252 286422 876909 161225 564835 425499 913383 110655 618735 724527 376406 856338 529833 428572 377393 750821 563566 323620 458378 936484 707084 916483 772236 038683 830439 265466 464754 500858 745567 122380 407686 755277 604504 677377 556126 672075 941751 055027 994236 595764 205057 767657 455147 747585 081987 099171 012494 060465 573241 227735 579343 736445 095407 321203 940093 285863 067901 069783 608393 487512 810168 663051 223724 844715 899771 095491 427041 023132 084289 495887 291064 733622 479743 971606 972214 180100 669874 199952 952865 980951 820909 435627 858496 253767 308672 814579 650964 148185 206425 733829 658690 066915 625317 896243 232612 405259 411175 139097 411459 779008 472468 785994 139926 350402 174137 718213 808631 719487 185958 821856 152036 777245 695643 521658 136731 505101 936536 256483 852505 > 92024 [i]
- extracting embedded OOA [i] would yield OOA(92024, 676, S9, 3, 1943), but