Best Known (178, 251, s)-Nets in Base 2
(178, 251, 138)-Net over F2 — Constructive and digital
Digital (178, 251, 138)-net over F2, using
- 1 times m-reduction [i] based on digital (178, 252, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 84, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- trace code for nets [i] based on digital (10, 84, 46)-net over F8, using
(178, 251, 233)-Net over F2 — Digital
Digital (178, 251, 233)-net over F2, using
(178, 251, 1706)-Net in Base 2 — Upper bound on s
There is no (178, 251, 1707)-net in base 2, because
- 1 times m-reduction [i] would yield (178, 250, 1707)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1844 372993 145627 500015 095468 346817 766512 591187 801470 927526 363868 764723 995610 > 2250 [i]