Best Known (65, 65+117, s)-Nets in Base 2
(65, 65+117, 43)-Net over F2 — Constructive and digital
Digital (65, 182, 43)-net over F2, using
- t-expansion [i] based on digital (59, 182, 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
(65, 65+117, 48)-Net over F2 — Digital
Digital (65, 182, 48)-net over F2, using
- net from sequence [i] based on digital (65, 47)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 65 and N(F) ≥ 48, using
(65, 65+117, 123)-Net in Base 2 — Upper bound on s
There is no (65, 182, 124)-net in base 2, because
- 1 times m-reduction [i] would yield (65, 181, 124)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 4 172674 251747 074945 711274 718132 138528 119977 533245 375793 > 2181 [i]