Best Known (18, 18+22, s)-Nets in Base 2
(18, 18+22, 17)-Net over F2 — Constructive and digital
Digital (18, 40, 17)-net over F2, using
- t-expansion [i] based on digital (15, 40, 17)-net over F2, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 15 and N(F) ≥ 17, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
(18, 18+22, 18)-Net over F2 — Digital
Digital (18, 40, 18)-net over F2, using
- net from sequence [i] based on digital (18, 17)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 18 and N(F) ≥ 18, using
(18, 18+22, 44)-Net in Base 2 — Upper bound on s
There is no (18, 40, 45)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(240, 45, S2, 22), but
- adding a parity check bit [i] would yield OA(241, 46, S2, 23), but
- the (dual) Plotkin bound shows that M ≥ 8 796093 022208 / 3 > 241 [i]
- adding a parity check bit [i] would yield OA(241, 46, S2, 23), but