Best Known (58−28, 58, s)-Nets in Base 2
(58−28, 58, 23)-Net over F2 — Constructive and digital
Digital (30, 58, 23)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (5, 19, 9)-net over F2, using
- net from sequence [i] based on digital (5, 8)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 5 and N(F) ≥ 9, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (5, 8)-sequence over F2, using
- digital (11, 39, 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 (5, 19, 9)-net over F2, using
(58−28, 58, 25)-Net over F2 — Digital
Digital (30, 58, 25)-net over F2, using
- t-expansion [i] based on digital (28, 58, 25)-net over F2, using
- net from sequence [i] based on digital (28, 24)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 28 and N(F) ≥ 25, using
- net from sequence [i] based on digital (28, 24)-sequence over F2, using
(58−28, 58, 75)-Net over F2 — Upper bound on s (digital)
There is no digital (30, 58, 76)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(258, 76, F2, 28) (dual of [76, 18, 29]-code), but
(58−28, 58, 77)-Net in Base 2 — Upper bound on s
There is no (30, 58, 78)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(258, 78, S2, 28), but
- the linear programming bound shows that M ≥ 6382 573449 503504 859136 / 19305 > 258 [i]