Best Known (14, 14+57, s)-Nets in Base 128
(14, 14+57, 288)-Net over F128 — Constructive and digital
Digital (14, 71, 288)-net over F128, using
- t-expansion [i] based on digital (9, 71, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
(14, 14+57, 353)-Net over F128 — Digital
Digital (14, 71, 353)-net over F128, using
- net from sequence [i] based on digital (14, 352)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 14 and N(F) ≥ 353, using
(14, 14+57, 16476)-Net in Base 128 — Upper bound on s
There is no (14, 71, 16477)-net in base 128, because
- 1 times m-reduction [i] would yield (14, 70, 16477)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 3199 421191 501061 915582 421510 916506 533728 598566 881140 655720 595621 171527 584134 218403 013541 529846 767912 553747 845886 561572 769572 220526 113207 729886 913861 > 12870 [i]