Best Known (51, 51+74, s)-Nets in Base 2
(51, 51+74, 36)-Net over F2 — Constructive and digital
Digital (51, 125, 36)-net over F2, using
- net from sequence [i] based on digital (51, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 3 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(51, 51+74, 40)-Net over F2 — Digital
Digital (51, 125, 40)-net over F2, using
- t-expansion [i] based on digital (50, 125, 40)-net over F2, using
- net from sequence [i] based on digital (50, 39)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 50 and N(F) ≥ 40, using
- net from sequence [i] based on digital (50, 39)-sequence over F2, using
(51, 51+74, 104)-Net in Base 2 — Upper bound on s
There is no (51, 125, 105)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 42 581492 236001 812032 112774 491882 603644 > 2125 [i]