Best Known (22, 22+22, s)-Nets in Base 2
(22, 22+22, 21)-Net over F2 — Constructive and digital
Digital (22, 44, 21)-net over F2, using
- t-expansion [i] based on digital (21, 44, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
(22, 22+22, 55)-Net over F2 — Upper bound on s (digital)
There is no digital (22, 44, 56)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(244, 56, F2, 22) (dual of [56, 12, 23]-code), but
- adding a parity check bit [i] would yield linear OA(245, 57, F2, 23) (dual of [57, 12, 24]-code), but
(22, 22+22, 57)-Net in Base 2 — Upper bound on s
There is no (22, 44, 58)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(244, 58, S2, 22), but
- the linear programming bound shows that M ≥ 30592 811531 239424 / 1539 > 244 [i]