Best Known (95, 190, s)-Nets in Base 2
(95, 190, 54)-Net over F2 — Constructive and digital
Digital (95, 190, 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, 190, 65)-Net over F2 — Digital
Digital (95, 190, 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, 190, 205)-Net over F2 — Upper bound on s (digital)
There is no digital (95, 190, 206)-net over F2, because
- 1 times m-reduction [i] would yield digital (95, 189, 206)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(2189, 206, F2, 94) (dual of [206, 17, 95]-code), but
- residual code [i] would yield OA(295, 111, S2, 47), but
- 1 times truncation [i] would yield OA(294, 110, S2, 46), but
- the linear programming bound shows that M ≥ 70 671520 962723 789133 441203 699712 / 3451 > 294 [i]
- 1 times truncation [i] would yield OA(294, 110, S2, 46), but
- residual code [i] would yield OA(295, 111, S2, 47), but
- extracting embedded orthogonal array [i] would yield linear OA(2189, 206, F2, 94) (dual of [206, 17, 95]-code), but
(95, 190, 234)-Net in Base 2 — Upper bound on s
There is no (95, 190, 235)-net in base 2, because
- 1 times m-reduction [i] would yield (95, 189, 235)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 791 101136 127672 545517 682637 874068 899811 483749 874079 501568 > 2189 [i]