Best Known (185−90, 185, s)-Nets in Base 2
(185−90, 185, 54)-Net over F2 — Constructive and digital
Digital (95, 185, 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]
(185−90, 185, 65)-Net over F2 — Digital
Digital (95, 185, 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
(185−90, 185, 208)-Net over F2 — Upper bound on s (digital)
There is no digital (95, 185, 209)-net over F2, because
- 6 times m-reduction [i] would yield digital (95, 179, 209)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(2179, 209, F2, 84) (dual of [209, 30, 85]-code), but
- adding a parity check bit [i] would yield linear OA(2180, 210, F2, 85) (dual of [210, 30, 86]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(2179, 209, F2, 84) (dual of [209, 30, 85]-code), but
(185−90, 185, 243)-Net in Base 2 — Upper bound on s
There is no (95, 185, 244)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 51 833897 943301 209332 839069 205760 816181 267153 885652 830532 > 2185 [i]