Best Known (133−73, 133, s)-Nets in Base 2
(133−73, 133, 43)-Net over F2 — Constructive and digital
Digital (60, 133, 43)-net over F2, using
- t-expansion [i] based on digital (59, 133, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
(133−73, 133, 129)-Net over F2 — Upper bound on s (digital)
There is no digital (60, 133, 130)-net over F2, because
- 9 times m-reduction [i] would yield digital (60, 124, 130)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(2124, 130, F2, 64) (dual of [130, 6, 65]-code), but
- 1 times code embedding in larger space [i] would yield linear OA(2125, 131, F2, 64) (dual of [131, 6, 65]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(2124, 130, F2, 64) (dual of [130, 6, 65]-code), but
(133−73, 133, 131)-Net in Base 2 — Upper bound on s
There is no (60, 133, 132)-net in base 2, because
- 13 times m-reduction [i] would yield (60, 120, 132)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2120, 132, S2, 60), but
- the linear programming bound shows that M ≥ 16503 694795 665515 477973 668460 440758 255616 / 10323 > 2120 [i]
- extracting embedded orthogonal array [i] would yield OA(2120, 132, S2, 60), but