Best Known (127, ∞, s)-Nets in Base 4
(127, ∞, 130)-Net over F4 — Constructive and digital
Digital (127, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (127, 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
(127, ∞, 176)-Net over F4 — Digital
Digital (127, m, 176)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (127, 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
(127, ∞, 397)-Net in Base 4 — Upper bound on s
There is no (127, m, 398)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (127, 1984, 398)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(41984, 398, S4, 5, 1857), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3376 101382 947613 974367 917454 010458 894778 092105 878982 800063 872233 186691 582491 895883 853483 790412 855855 295209 873497 669702 708323 369609 113931 518491 396842 934983 419813 015937 997395 603908 660753 408724 750168 678632 056497 611556 601571 321570 644065 081609 928378 572184 760622 316186 662228 915836 897315 792307 410266 905094 744637 641102 595955 275346 720525 014733 839317 908719 748696 757333 348435 846097 186845 387179 459803 286505 916949 040199 829096 963092 211042 502601 342085 773584 797119 661443 289086 754247 844084 163127 475088 324390 231987 653713 501843 720612 934247 296657 275336 821727 838362 139189 601761 071082 823989 646433 836605 870896 985326 707945 596245 648170 078254 656290 948507 332623 508445 341895 844305 184394 173038 516978 016804 495706 030565 630070 362743 397602 208756 390471 647563 994289 823914 924001 344441 673956 571461 549982 736041 729075 469119 889521 350103 686661 319543 175725 750178 394800 209153 901971 145675 934767 641621 107952 365444 700251 735650 952591 647887 445183 767193 696344 351868 346628 236627 389839 847625 299960 822347 210800 085904 510549 913821 192494 425730 880630 171142 863892 192261 791695 850987 854403 254416 918812 260025 313124 111527 259197 537956 161163 702372 639441 351961 948350 803834 085020 928642 094130 259931 835406 568585 052733 923378 556204 817502 772659 322005 579945 341458 841600 / 929 > 41984 [i]
- extracting embedded OOA [i] would yield OOA(41984, 398, S4, 5, 1857), but