Best Known (133, ∞, s)-Nets in Base 4
(133, ∞, 130)-Net over F4 — Constructive and digital
Digital (133, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (133, 129)-sequence over F4, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
(133, ∞, 176)-Net over F4 — Digital
Digital (133, m, 176)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (133, 175)-sequence over F4, using
- t-expansion [i] based on digital (125, 175)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 125 and N(F) ≥ 176, using
- t-expansion [i] based on digital (125, 175)-sequence over F4, using
(133, ∞, 415)-Net in Base 4 — Upper bound on s
There is no (133, m, 416)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (133, 2074, 416)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42074, 416, S4, 5, 1941), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5117 418202 352433 088362 584171 029838 939822 737847 541449 296790 325546 408189 625729 753260 681067 392739 980194 469018 159358 559345 302144 490684 903600 520557 070816 922119 222505 383944 163123 926589 257264 040359 425495 086030 957689 173946 188894 180937 360324 053609 255098 817651 267757 535434 334993 579956 315637 178977 837876 996946 317764 277706 306689 766854 980099 929155 392713 319114 137837 110416 665376 836726 440527 969430 197607 393309 127180 703764 173413 138009 778815 878234 248178 725599 208101 510286 784382 315832 910456 983159 320036 407874 013851 555170 444187 081568 766739 903931 925769 422858 014689 092623 145165 568780 304578 380011 045824 939061 762267 107546 022702 606356 912458 253468 074151 265428 017748 993326 789854 700108 756628 243388 252449 511183 129684 933629 940837 782267 551791 984073 681632 747039 814915 999014 219334 785388 235983 444623 195486 448639 891550 368064 133573 728158 521961 917919 180292 522680 512048 783787 851256 253947 589231 661438 209650 088919 167037 832064 273512 134339 868583 964149 101243 624434 577562 686623 326757 828176 728920 117967 323713 320507 709738 664645 351415 763008 316264 926690 872420 389085 930309 375760 963324 233548 827020 375251 599497 834725 759063 058544 977131 019233 945553 762545 121225 621189 752402 292433 036175 101339 793394 635458 683661 556559 545145 465694 014872 597732 231455 904928 020818 947295 116873 199422 213488 567207 293538 097302 601728 / 971 > 42074 [i]
- extracting embedded OOA [i] would yield OOA(42074, 416, S4, 5, 1941), but