Best Known (74, 74+22, s)-Nets in Base 8
(74, 74+22, 2979)-Net over F8 — Constructive and digital
Digital (74, 96, 2979)-net over F8, using
- net defined by OOA [i] based on linear OOA(896, 2979, F8, 22, 22) (dual of [(2979, 22), 65442, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(896, 32769, F8, 22) (dual of [32769, 32673, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(896, 32773, F8, 22) (dual of [32773, 32677, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(896, 32768, F8, 22) (dual of [32768, 32672, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(891, 32768, F8, 21) (dual of [32768, 32677, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(80, 5, F8, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(896, 32773, F8, 22) (dual of [32773, 32677, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(896, 32769, F8, 22) (dual of [32769, 32673, 23]-code), using
(74, 74+22, 23103)-Net over F8 — Digital
Digital (74, 96, 23103)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(896, 23103, F8, 22) (dual of [23103, 23007, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(896, 32768, F8, 22) (dual of [32768, 32672, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(896, 32768, F8, 22) (dual of [32768, 32672, 23]-code), using
(74, 74+22, large)-Net in Base 8 — Upper bound on s
There is no (74, 96, large)-net in base 8, because
- 20 times m-reduction [i] would yield (74, 76, large)-net in base 8, but