Best Known (38−18, 38, s)-Nets in Base 2
(38−18, 38, 20)-Net over F2 — Constructive and digital
Digital (20, 38, 20)-net over F2, using
- t-expansion [i] based on digital (19, 38, 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
(38−18, 38, 58)-Net over F2 — Upper bound on s (digital)
There is no digital (20, 38, 59)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(238, 59, F2, 18) (dual of [59, 21, 19]-code), but
- adding a parity check bit [i] would yield linear OA(239, 60, F2, 19) (dual of [60, 21, 20]-code), but
(38−18, 38, 63)-Net in Base 2 — Upper bound on s
There is no (20, 38, 64)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(238, 64, S2, 18), but
- the linear programming bound shows that M ≥ 1638 822081 200128 / 5865 > 238 [i]