Best Known (23, 23+20, s)-Nets in Base 2
(23, 23+20, 21)-Net over F2 — Constructive and digital
Digital (23, 43, 21)-net over F2, using
- t-expansion [i] based on digital (21, 43, 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
(23, 23+20, 22)-Net over F2 — Digital
Digital (23, 43, 22)-net over F2, using
- net from sequence [i] based on digital (23, 21)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 23 and N(F) ≥ 22, using
(23, 23+20, 73)-Net over F2 — Upper bound on s (digital)
There is no digital (23, 43, 74)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(243, 74, F2, 20) (dual of [74, 31, 21]-code), but
(23, 23+20, 75)-Net in Base 2 — Upper bound on s
There is no (23, 43, 76)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 9 116222 870339 > 243 [i]
- extracting embedded orthogonal array [i] would yield OA(243, 76, S2, 20), but
- the linear programming bound shows that M ≥ 665794 267232 060016 383085 248512 / 74619 439776 078197 > 243 [i]