Best Known (161, 183, s)-Nets in Base 2
(161, 183, 5961)-Net over F2 — Constructive and digital
Digital (161, 183, 5961)-net over F2, using
- net defined by OOA [i] based on linear OOA(2183, 5961, F2, 22, 22) (dual of [(5961, 22), 130959, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2183, 65571, F2, 22) (dual of [65571, 65388, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2183, 65574, F2, 22) (dual of [65574, 65391, 23]-code), using
- 1 times truncation [i] based on linear OA(2184, 65575, F2, 23) (dual of [65575, 65391, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2177, 65536, F2, 23) (dual of [65536, 65359, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(27, 39, F2, 3) (dual of [39, 32, 4]-code or 39-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- 1 times truncation [i] based on linear OA(2184, 65575, F2, 23) (dual of [65575, 65391, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2183, 65574, F2, 22) (dual of [65574, 65391, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2183, 65571, F2, 22) (dual of [65571, 65388, 23]-code), using
(161, 183, 13114)-Net over F2 — Digital
Digital (161, 183, 13114)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2183, 13114, F2, 5, 22) (dual of [(13114, 5), 65387, 23]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2183, 65570, F2, 22) (dual of [65570, 65387, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2183, 65574, F2, 22) (dual of [65574, 65391, 23]-code), using
- 1 times truncation [i] based on linear OA(2184, 65575, F2, 23) (dual of [65575, 65391, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2177, 65536, F2, 23) (dual of [65536, 65359, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(27, 39, F2, 3) (dual of [39, 32, 4]-code or 39-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- 1 times truncation [i] based on linear OA(2184, 65575, F2, 23) (dual of [65575, 65391, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2183, 65574, F2, 22) (dual of [65574, 65391, 23]-code), using
- OOA 5-folding [i] based on linear OA(2183, 65570, F2, 22) (dual of [65570, 65387, 23]-code), using
(161, 183, 500086)-Net in Base 2 — Upper bound on s
There is no (161, 183, 500087)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 12 260222 091463 089622 562142 315282 771543 354089 870449 568804 > 2183 [i]