Best Known (96, 124, s)-Nets in Base 8
(96, 124, 2341)-Net over F8 — Constructive and digital
Digital (96, 124, 2341)-net over F8, using
- 82 times duplication [i] based on digital (94, 122, 2341)-net over F8, using
- net defined by OOA [i] based on linear OOA(8122, 2341, F8, 28, 28) (dual of [(2341, 28), 65426, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(8122, 32774, F8, 28) (dual of [32774, 32652, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8122, 32779, F8, 28) (dual of [32779, 32657, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(8121, 32768, F8, 28) (dual of [32768, 32647, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(8122, 32779, F8, 28) (dual of [32779, 32657, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(8122, 32774, F8, 28) (dual of [32774, 32652, 29]-code), using
- net defined by OOA [i] based on linear OOA(8122, 2341, F8, 28, 28) (dual of [(2341, 28), 65426, 29]-NRT-code), using
(96, 124, 28201)-Net over F8 — Digital
Digital (96, 124, 28201)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8124, 28201, F8, 28) (dual of [28201, 28077, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8124, 32786, F8, 28) (dual of [32786, 32662, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(8121, 32768, F8, 28) (dual of [32768, 32647, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(27) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(8124, 32786, F8, 28) (dual of [32786, 32662, 29]-code), using
(96, 124, large)-Net in Base 8 — Upper bound on s
There is no (96, 124, large)-net in base 8, because
- 26 times m-reduction [i] would yield (96, 98, large)-net in base 8, but