Best Known (73, 73+74, s)-Nets in Base 2
(73, 73+74, 49)-Net over F2 — Constructive and digital
Digital (73, 147, 49)-net over F2, using
- t-expansion [i] based on digital (70, 147, 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
(73, 73+74, 157)-Net over F2 — Upper bound on s (digital)
There is no digital (73, 147, 158)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2147, 158, F2, 74) (dual of [158, 11, 75]-code), but
- residual code [i] would yield linear OA(273, 83, F2, 37) (dual of [83, 10, 38]-code), but
(73, 73+74, 180)-Net in Base 2 — Upper bound on s
There is no (73, 147, 181)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 196 469911 897924 635805 383756 040370 586603 866038 > 2147 [i]