Best Known (183−115, 183, s)-Nets in Base 2
(183−115, 183, 43)-Net over F2 — Constructive and digital
Digital (68, 183, 43)-net over F2, using
- t-expansion [i] based on digital (59, 183, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
(183−115, 183, 49)-Net over F2 — Digital
Digital (68, 183, 49)-net over F2, using
- net from sequence [i] based on digital (68, 48)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 68 and N(F) ≥ 49, using
(183−115, 183, 130)-Net in Base 2 — Upper bound on s
There is no (68, 183, 131)-net in base 2, because
- 1 times m-reduction [i] would yield (68, 182, 131)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 7 468906 992550 810994 350661 201273 407767 519608 566598 816448 > 2182 [i]