Best Known (167−102, 167, s)-Nets in Base 2
(167−102, 167, 43)-Net over F2 — Constructive and digital
Digital (65, 167, 43)-net over F2, using
- t-expansion [i] based on digital (59, 167, 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
(167−102, 167, 48)-Net over F2 — Digital
Digital (65, 167, 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
(167−102, 167, 127)-Net in Base 2 — Upper bound on s
There is no (65, 167, 128)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 214 383568 629809 005246 580263 724730 375366 020496 168141 > 2167 [i]