Best Known (82, 82+∞, s)-Nets in Base 5
(82, 82+∞, 82)-Net over F5 — Constructive and digital
Digital (82, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (82, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
(82, 82+∞, 150)-Net over F5 — Digital
Digital (82, m, 150)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (82, 149)-sequence over F5, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 76 and N(F) ≥ 150, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
(82, 82+∞, 346)-Net in Base 5 — Upper bound on s
There is no (82, m, 347)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (82, 1383, 347)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51383, 347, S5, 4, 1301), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4523 966374 849868 956534 983183 516868 254553 534702 339072 875066 023693 288272 268702 772825 142929 791995 236787 748432 478335 813729 059547 649855 506902 421082 371439 097706 034566 157315 805632 948396 640164 735718 721790 262763 797552 949725 276786 531985 071448 267397 856904 577005 934172 825223 973095 422482 426597 805376 593552 381789 231508 807817 323917 229878 714905 008778 465152 344382 463742 105151 179541 559357 865052 206528 734795 162224 457326 345409 445262 391018 816018 556409 745731 183046 917502 673546 967110 263757 812717 772151 028891 457181 968607 349320 392812 075578 735890 005154 600211 521653 256629 453205 935747 113625 060659 010755 712096 834895 314971 155944 253176 885327 669971 554915 769232 051179 099265 466557 809844 789017 981601 508480 519085 511201 660452 966497 757826 457622 327423 790725 742779 493211 106214 356070 941859 853487 261694 828456 809009 650866 470661 379717 296401 396520 411444 092752 122078 772083 616945 585947 482563 702992 062041 623907 174076 167899 540804 702167 804360 820858 291055 521294 336723 016234 948365 442425 366467 205094 522796 571254 730224 609375 / 651 > 51383 [i]
- extracting embedded OOA [i] would yield OOA(51383, 347, S5, 4, 1301), but