Best Known (177−114, 177, s)-Nets in Base 2
(177−114, 177, 43)-Net over F2 — Constructive and digital
Digital (63, 177, 43)-net over F2, using
- t-expansion [i] based on digital (59, 177, 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
(177−114, 177, 44)-Net over F2 — Digital
Digital (63, 177, 44)-net over F2, using
- t-expansion [i] based on digital (62, 177, 44)-net over F2, using
- net from sequence [i] based on digital (62, 43)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 62 and N(F) ≥ 44, using
- net from sequence [i] based on digital (62, 43)-sequence over F2, using
(177−114, 177, 119)-Net in Base 2 — Upper bound on s
There is no (63, 177, 120)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 253473 986051 729579 973691 963258 573339 595698 646603 257720 > 2177 [i]