Best Known (132, 150, s)-Nets in Base 2
(132, 150, 7285)-Net over F2 — Constructive and digital
Digital (132, 150, 7285)-net over F2, using
- net defined by OOA [i] based on linear OOA(2150, 7285, F2, 18, 18) (dual of [(7285, 18), 130980, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2150, 65565, F2, 18) (dual of [65565, 65415, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2150, 65567, F2, 18) (dual of [65567, 65417, 19]-code), using
- 1 times truncation [i] based on linear OA(2151, 65568, F2, 19) (dual of [65568, 65417, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(2145, 65536, F2, 19) (dual of [65536, 65391, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2113, 65536, F2, 15) (dual of [65536, 65423, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- 1 times truncation [i] based on linear OA(2151, 65568, F2, 19) (dual of [65568, 65417, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2150, 65567, F2, 18) (dual of [65567, 65417, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(2150, 65565, F2, 18) (dual of [65565, 65415, 19]-code), using
(132, 150, 13602)-Net over F2 — Digital
Digital (132, 150, 13602)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2150, 13602, F2, 4, 18) (dual of [(13602, 4), 54258, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2150, 16391, F2, 4, 18) (dual of [(16391, 4), 65414, 19]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2150, 65564, F2, 18) (dual of [65564, 65414, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2150, 65567, F2, 18) (dual of [65567, 65417, 19]-code), using
- 1 times truncation [i] based on linear OA(2151, 65568, F2, 19) (dual of [65568, 65417, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(2145, 65536, F2, 19) (dual of [65536, 65391, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2113, 65536, F2, 15) (dual of [65536, 65423, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- 1 times truncation [i] based on linear OA(2151, 65568, F2, 19) (dual of [65568, 65417, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2150, 65567, F2, 18) (dual of [65567, 65417, 19]-code), using
- OOA 4-folding [i] based on linear OA(2150, 65564, F2, 18) (dual of [65564, 65414, 19]-code), using
- discarding factors / shortening the dual code based on linear OOA(2150, 16391, F2, 4, 18) (dual of [(16391, 4), 65414, 19]-NRT-code), using
(132, 150, 431424)-Net in Base 2 — Upper bound on s
There is no (132, 150, 431425)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1427 258085 302824 951002 935363 744695 188955 597936 > 2150 [i]