Best Known (230−51, 230, s)-Nets in Base 2
(230−51, 230, 260)-Net over F2 — Constructive and digital
Digital (179, 230, 260)-net over F2, using
- 22 times duplication [i] based on digital (177, 228, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 57, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 57, 65)-net over F16, using
(230−51, 230, 432)-Net over F2 — Digital
Digital (179, 230, 432)-net over F2, using
(230−51, 230, 5784)-Net in Base 2 — Upper bound on s
There is no (179, 230, 5785)-net in base 2, because
- 1 times m-reduction [i] would yield (179, 229, 5785)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 862 898232 301522 277432 371923 808639 908334 537084 429306 758218 077033 087298 > 2229 [i]