Best Known (19, 40, s)-Nets in Base 2
(19, 40, 20)-Net over F2 — Constructive and digital
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
(19, 40, 47)-Net over F2 — Upper bound on s (digital)
There is no digital (19, 40, 48)-net over F2, because
- 1 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, 40, 50)-Net in Base 2 — Upper bound on s
There is no (19, 40, 51)-net in base 2, because
- 1 times m-reduction [i] would yield (19, 39, 51)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(239, 51, S2, 20), but
- the linear programming bound shows that M ≥ 23503 160555 339776 / 40425 > 239 [i]
- extracting embedded orthogonal array [i] would yield OA(239, 51, S2, 20), but