Best Known (37, 37+36, s)-Nets in Base 2
(37, 37+36, 25)-Net over F2 — Constructive and digital
Digital (37, 73, 25)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (8, 26, 11)-net over F2, using
- net from sequence [i] based on digital (8, 10)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 8 and N(F) ≥ 11, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (8, 10)-sequence over F2, using
- digital (11, 47, 14)-net over F2, using
- net from sequence [i] based on digital (11, 13)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 11 and N(F) ≥ 14, using
- net from sequence [i] based on digital (11, 13)-sequence over F2, using
- digital (8, 26, 11)-net over F2, using
(37, 37+36, 30)-Net over F2 — Digital
Digital (37, 73, 30)-net over F2, using
- t-expansion [i] based on digital (36, 73, 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
- net from sequence [i] based on digital (36, 29)-sequence over F2, using
(37, 37+36, 85)-Net over F2 — Upper bound on s (digital)
There is no digital (37, 73, 86)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(273, 86, F2, 36) (dual of [86, 13, 37]-code), but
(37, 37+36, 87)-Net in Base 2 — Upper bound on s
There is no (37, 73, 88)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(273, 88, S2, 36), but
- the linear programming bound shows that M ≥ 793 659800 577004 053194 604544 / 82593 > 273 [i]