Best Known (85−42, 85, s)-Nets in Base 2
(85−42, 85, 33)-Net over F2 — Constructive and digital
Digital (43, 85, 33)-net over F2, using
- t-expansion [i] based on digital (39, 85, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
(85−42, 85, 34)-Net over F2 — Digital
Digital (43, 85, 34)-net over F2, using
- net from sequence [i] based on digital (43, 33)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 43 and N(F) ≥ 34, using
(85−42, 85, 98)-Net over F2 — Upper bound on s (digital)
There is no digital (43, 85, 99)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(285, 99, F2, 42) (dual of [99, 14, 43]-code), but
(85−42, 85, 99)-Net in Base 2 — Upper bound on s
There is no (43, 85, 100)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(285, 100, S2, 42), but
- the linear programming bound shows that M ≥ 176638 569355 532697 974668 787712 / 4433 > 285 [i]