Best Known (20, 20+22, s)-Nets in Base 2
(20, 20+22, 20)-Net over F2 — Constructive and digital
Digital (20, 42, 20)-net over F2, using
- t-expansion [i] based on digital (19, 42, 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+22, 48)-Net over F2 — Upper bound on s (digital)
There is no digital (20, 42, 49)-net over F2, because
- 2 times m-reduction [i] would yield digital (20, 40, 49)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(240, 49, F2, 20) (dual of [49, 9, 21]-code), but
(20, 20+22, 50)-Net in Base 2 — Upper bound on s
There is no (20, 42, 51)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(242, 51, S2, 22), but
- the linear programming bound shows that M ≥ 246 290604 621824 / 45 > 242 [i]