Best Known (55−42, 55, s)-Nets in Base 128
(55−42, 55, 288)-Net over F128 — Constructive and digital
Digital (13, 55, 288)-net over F128, using
- t-expansion [i] based on digital (9, 55, 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
(55−42, 55, 321)-Net over F128 — Digital
Digital (13, 55, 321)-net over F128, using
- t-expansion [i] based on digital (12, 55, 321)-net over F128, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 12 and N(F) ≥ 321, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
(55−42, 55, 22561)-Net in Base 128 — Upper bound on s
There is no (13, 55, 22562)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 78 808226 628590 710914 141378 508713 700981 484551 726793 602816 636914 419828 107276 534966 621866 812527 575422 546678 161267 933400 > 12855 [i]