Best Known (36, 36+36, s)-Nets in Base 2
(36, 36+36, 24)-Net over F2 — Constructive and digital
Digital (36, 72, 24)-net over F2, using
- t-expansion [i] based on digital (33, 72, 24)-net over F2, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 24, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
(36, 36+36, 30)-Net over F2 — Digital
Digital (36, 72, 30)-net over F2, using
- net from sequence [i] based on digital (36, 29)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 36 and N(F) ≥ 30, using
(36, 36+36, 81)-Net over F2 — Upper bound on s (digital)
There is no digital (36, 72, 82)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(272, 82, F2, 36) (dual of [82, 10, 37]-code), but
- adding a parity check bit [i] would yield linear OA(273, 83, F2, 37) (dual of [83, 10, 38]-code), but
(36, 36+36, 85)-Net in Base 2 — Upper bound on s
There is no (36, 72, 86)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(272, 86, S2, 36), but
- the linear programming bound shows that M ≥ 68 455424 535678 377017 737216 / 13547 > 272 [i]