Best Known (91−14, 91, s)-Nets in Base 8
(91−14, 91, 299599)-Net over F8 — Constructive and digital
Digital (77, 91, 299599)-net over F8, using
- net defined by OOA [i] based on linear OOA(891, 299599, F8, 14, 14) (dual of [(299599, 14), 4194295, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(891, 2097193, F8, 14) (dual of [2097193, 2097102, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(850, 2097152, F8, 9) (dual of [2097152, 2097102, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(86, 41, F8, 4) (dual of [41, 35, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
- OA 7-folding and stacking [i] based on linear OA(891, 2097193, F8, 14) (dual of [2097193, 2097102, 15]-code), using
(91−14, 91, 2097193)-Net over F8 — Digital
Digital (77, 91, 2097193)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(891, 2097193, F8, 14) (dual of [2097193, 2097102, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(850, 2097152, F8, 9) (dual of [2097152, 2097102, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(86, 41, F8, 4) (dual of [41, 35, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
(91−14, 91, large)-Net in Base 8 — Upper bound on s
There is no (77, 91, large)-net in base 8, because
- 12 times m-reduction [i] would yield (77, 79, large)-net in base 8, but