Best Known (95, 95+92, s)-Nets in Base 2
(95, 95+92, 54)-Net over F2 — Constructive and digital
Digital (95, 187, 54)-net over F2, using
- net from sequence [i] based on digital (95, 53)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 5 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
(95, 95+92, 65)-Net over F2 — Digital
Digital (95, 187, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
(95, 95+92, 207)-Net over F2 — Upper bound on s (digital)
There is no digital (95, 187, 208)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2187, 208, F2, 92) (dual of [208, 21, 93]-code), but
- residual code [i] would yield OA(295, 115, S2, 46), but
- the linear programming bound shows that M ≥ 2283 038731 011041 152095 562472 882176 / 53669 > 295 [i]
- residual code [i] would yield OA(295, 115, S2, 46), but
(95, 95+92, 239)-Net in Base 2 — Upper bound on s
There is no (95, 187, 240)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 224 483601 909967 961043 905390 792579 224177 474200 804492 273709 > 2187 [i]