Best Known (67, 67+122, s)-Nets in Base 2
(67, 67+122, 43)-Net over F2 — Constructive and digital
Digital (67, 189, 43)-net over F2, using
- t-expansion [i] based on digital (59, 189, 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
(67, 67+122, 48)-Net over F2 — Digital
Digital (67, 189, 48)-net over F2, using
- t-expansion [i] based on digital (65, 189, 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
- net from sequence [i] based on digital (65, 47)-sequence over F2, using
(67, 67+122, 126)-Net in Base 2 — Upper bound on s
There is no (67, 189, 127)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1078 785394 811887 333853 197125 830077 796577 721206 236038 605748 > 2189 [i]