Best Known (178, 178+72, s)-Nets in Base 2
(178, 178+72, 144)-Net over F2 — Constructive and digital
Digital (178, 250, 144)-net over F2, using
- 21 times duplication [i] based on digital (177, 249, 144)-net over F2, using
- trace code for nets [i] based on digital (11, 83, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- trace code for nets [i] based on digital (11, 83, 48)-net over F8, using
(178, 178+72, 238)-Net over F2 — Digital
Digital (178, 250, 238)-net over F2, using
(178, 178+72, 1706)-Net in Base 2 — Upper bound on s
There is no (178, 250, 1707)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1844 372993 145627 500015 095468 346817 766512 591187 801470 927526 363868 764723 995610 > 2250 [i]