Best Known (20, 20+20, s)-Nets in Base 2
(20, 20+20, 20)-Net over F2 — Constructive and digital
Digital (20, 40, 20)-net over F2, using
- t-expansion [i] based on digital (19, 40, 20)-net over F2, using
- net from sequence [i] based on digital (19, 19)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 19 and N(F) ≥ 20, using
- net from sequence [i] based on digital (19, 19)-sequence over F2, using
(20, 20+20, 48)-Net over F2 — Upper bound on s (digital)
There is no digital (20, 40, 49)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(240, 49, F2, 20) (dual of [49, 9, 21]-code), but
(20, 20+20, 53)-Net in Base 2 — Upper bound on s
There is no (20, 40, 54)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(240, 54, S2, 20), but
- the linear programming bound shows that M ≥ 140 737488 355328 / 119 > 240 [i]