Best Known (94, 122, s)-Nets in Base 8
(94, 122, 2341)-Net over F8 — Constructive and digital
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
(94, 122, 24030)-Net over F8 — Digital
Digital (94, 122, 24030)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8122, 24030, F8, 28) (dual of [24030, 23908, 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
(94, 122, large)-Net in Base 8 — Upper bound on s
There is no (94, 122, large)-net in base 8, because
- 26 times m-reduction [i] would yield (94, 96, large)-net in base 8, but