Best Known (131, 131+38, s)-Nets in Base 8
(131, 131+38, 1725)-Net over F8 — Constructive and digital
Digital (131, 169, 1725)-net over F8, using
- 82 times duplication [i] based on digital (129, 167, 1725)-net over F8, using
- net defined by OOA [i] based on linear OOA(8167, 1725, F8, 38, 38) (dual of [(1725, 38), 65383, 39]-NRT-code), using
- OA 19-folding and stacking [i] based on linear OA(8167, 32775, F8, 38) (dual of [32775, 32608, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(8167, 32779, F8, 38) (dual of [32779, 32612, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(35) [i] based on
- linear OA(8166, 32768, F8, 38) (dual of [32768, 32602, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(8156, 32768, F8, 36) (dual of [32768, 32612, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(37) ⊂ Ce(35) [i] based on
- discarding factors / shortening the dual code based on linear OA(8167, 32779, F8, 38) (dual of [32779, 32612, 39]-code), using
- OA 19-folding and stacking [i] based on linear OA(8167, 32775, F8, 38) (dual of [32775, 32608, 39]-code), using
- net defined by OOA [i] based on linear OOA(8167, 1725, F8, 38, 38) (dual of [(1725, 38), 65383, 39]-NRT-code), using
(131, 131+38, 32786)-Net over F8 — Digital
Digital (131, 169, 32786)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8169, 32786, F8, 38) (dual of [32786, 32617, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(34) [i] based on
- linear OA(8166, 32768, F8, 38) (dual of [32768, 32602, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(8151, 32768, F8, 35) (dual of [32768, 32617, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(83, 18, F8, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(37) ⊂ Ce(34) [i] based on
(131, 131+38, large)-Net in Base 8 — Upper bound on s
There is no (131, 169, large)-net in base 8, because
- 36 times m-reduction [i] would yield (131, 133, large)-net in base 8, but