Best Known (129, ∞, s)-Nets in Base 4
(129, ∞, 130)-Net over F4 — Constructive and digital
Digital (129, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (129, 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
(129, ∞, 176)-Net over F4 — Digital
Digital (129, m, 176)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (129, 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
(129, ∞, 403)-Net in Base 4 — Upper bound on s
There is no (129, m, 404)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (129, 2014, 404)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42014, 404, S4, 5, 1885), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3878 225777 456371 898827 396695 014515 496103 123197 812079 071969 751029 304851 870380 842183 047252 574691 541711 921403 756481 435248 456719 667635 294563 555032 930271 809826 768865 156741 892193 130445 230327 271412 170923 909115 987387 200860 028748 364952 357132 956556 040734 188165 046259 690003 501326 891603 041894 928528 893999 484626 298417 878977 103831 809146 761316 541813 766809 117891 174534 504812 839887 085421 919059 357838 438365 067474 070536 805650 410600 458818 759190 471996 038277 272548 875274 294884 910289 011172 234469 684586 429291 286208 194061 972461 770550 069444 817698 573918 352496 273498 193157 037788 571036 915239 752857 724410 330026 803432 300646 417949 820571 515359 184909 855011 711805 511515 474918 280040 115420 805173 929236 823519 723204 430875 341806 682242 514632 644459 310543 158398 078940 879839 673114 326642 736671 916161 204246 693943 586293 569779 256173 010723 550969 852319 758721 785516 245608 973468 338683 912355 385264 594393 293026 776566 094611 960250 653017 973128 947679 795472 197528 486782 140566 990083 217502 374484 592460 028363 051107 846547 786144 408284 552157 879788 998835 527576 436539 587152 790420 263585 633203 784797 222587 884546 855808 982642 474670 578324 920965 509099 893771 398977 891391 218300 815094 076836 751216 837899 739975 425935 938464 721334 860481 533340 530923 078760 573454 677984 914381 297200 394699 664865 099776 / 943 > 42014 [i]
- extracting embedded OOA [i] would yield OOA(42014, 404, S4, 5, 1885), but