Best Known (76−14, 76, s)-Nets in Base 8
(76−14, 76, 37452)-Net over F8 — Constructive and digital
Digital (62, 76, 37452)-net over F8, using
- net defined by OOA [i] based on linear OOA(876, 37452, F8, 14, 14) (dual of [(37452, 14), 524252, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(876, 262164, F8, 14) (dual of [262164, 262088, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(876, 262165, F8, 14) (dual of [262165, 262089, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(873, 262144, F8, 14) (dual of [262144, 262071, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(855, 262144, F8, 11) (dual of [262144, 262089, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(83, 21, F8, 2) (dual of [21, 18, 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(13) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(876, 262165, F8, 14) (dual of [262165, 262089, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(876, 262164, F8, 14) (dual of [262164, 262088, 15]-code), using
(76−14, 76, 262165)-Net over F8 — Digital
Digital (62, 76, 262165)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(876, 262165, F8, 14) (dual of [262165, 262089, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(873, 262144, F8, 14) (dual of [262144, 262071, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(855, 262144, F8, 11) (dual of [262144, 262089, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(83, 21, F8, 2) (dual of [21, 18, 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(13) ⊂ Ce(10) [i] based on
(76−14, 76, large)-Net in Base 8 — Upper bound on s
There is no (62, 76, large)-net in base 8, because
- 12 times m-reduction [i] would yield (62, 64, large)-net in base 8, but