Best Known (74, 74+55, s)-Nets in Base 2
(74, 74+55, 49)-Net over F2 — Constructive and digital
Digital (74, 129, 49)-net over F2, using
- t-expansion [i] based on digital (70, 129, 49)-net over F2, using
- net from sequence [i] based on digital (70, 48)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, and 1 place with degree 2 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (70, 48)-sequence over F2, using
(74, 74+55, 56)-Net over F2 — Digital
Digital (74, 129, 56)-net over F2, using
(74, 74+55, 254)-Net in Base 2 — Upper bound on s
There is no (74, 129, 255)-net in base 2, because
- 1 times m-reduction [i] would yield (74, 128, 255)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 359 397167 305450 321603 052202 838698 887942 > 2128 [i]