Best Known (23−13, 23, s)-Nets in Base 2
(23−13, 23, 12)-Net over F2 — Constructive and digital
Digital (10, 23, 12)-net over F2, using
- t-expansion [i] based on digital (9, 23, 12)-net over F2, using
- net from sequence [i] based on digital (9, 11)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 9 and N(F) ≥ 12, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (9, 11)-sequence over F2, using
(23−13, 23, 13)-Net over F2 — Digital
Digital (10, 23, 13)-net over F2, using
- net from sequence [i] based on digital (10, 12)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 10 and N(F) ≥ 13, using
(23−13, 23, 25)-Net in Base 2 — Upper bound on s
There is no (10, 23, 26)-net in base 2, because
- extracting embedded OOA [i] would yield OOA(223, 26, S2, 2, 13), but
- the linear programming bound for OOAs shows that M ≥ 696137 023488 / 72653 > 223 [i]