Best Known (19, 41, s)-Nets in Base 2
(19, 41, 20)-Net over F2 — Constructive and digital
Digital (19, 41, 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
(19, 41, 47)-Net over F2 — Upper bound on s (digital)
There is no digital (19, 41, 48)-net over F2, because
- 2 times m-reduction [i] would yield digital (19, 39, 48)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(239, 48, F2, 20) (dual of [48, 9, 21]-code), but
- 1 times code embedding in larger space [i] would yield linear OA(240, 49, F2, 20) (dual of [49, 9, 21]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(239, 48, F2, 20) (dual of [48, 9, 21]-code), but
(19, 41, 48)-Net in Base 2 — Upper bound on s
There is no (19, 41, 49)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(241, 49, S2, 22), but
- the linear programming bound shows that M ≥ 45 629732 552704 / 17 > 241 [i]