Best Known (35, 35+∞, s)-Nets in Base 4
(35, 35+∞, 56)-Net over F4 — Constructive and digital
Digital (35, m, 56)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (35, 55)-sequence over F4, using
- t-expansion [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 from the 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) = 33 and N(F) ≥ 56, using
- t-expansion [i] based on digital (33, 55)-sequence over F4, using
(35, 35+∞, 65)-Net over F4 — Digital
Digital (35, m, 65)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (35, 64)-sequence over F4, using
- t-expansion [i] based on digital (33, 64)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 65, using
- t-expansion [i] based on digital (33, 64)-sequence over F4, using
(35, 35+∞, 118)-Net in Base 4 — Upper bound on s
There is no (35, m, 119)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (35, 471, 119)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4471, 119, S4, 4, 436), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 19479 921501 058958 122654 618725 763697 337719 508641 738067 413630 611357 038822 608801 297293 441704 919899 648192 726363 281651 527946 960955 066716 638264 772059 880612 441369 597756 918009 861724 348649 191968 829300 353000 133464 748803 827399 487508 060100 229154 857996 118567 420887 457790 881449 285257 991326 069472 362496 / 437 > 4471 [i]
- extracting embedded OOA [i] would yield OOA(4471, 119, S4, 4, 436), but