Best Known (91−17, 91, s)-Nets in Base 8
(91−17, 91, 32771)-Net over F8 — Constructive and digital
Digital (74, 91, 32771)-net over F8, using
- net defined by OOA [i] based on linear OOA(891, 32771, F8, 17, 17) (dual of [(32771, 17), 557016, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(891, 262169, F8, 17) (dual of [262169, 262078, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(891, 262174, F8, 17) (dual of [262174, 262083, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- linear OA(885, 262144, F8, 17) (dual of [262144, 262059, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(861, 262144, F8, 12) (dual of [262144, 262083, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(86, 30, F8, 4) (dual of [30, 24, 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(16) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(891, 262174, F8, 17) (dual of [262174, 262083, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(891, 262169, F8, 17) (dual of [262169, 262078, 18]-code), using
(91−17, 91, 240543)-Net over F8 — Digital
Digital (74, 91, 240543)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(891, 240543, F8, 17) (dual of [240543, 240452, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(891, 262174, F8, 17) (dual of [262174, 262083, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- linear OA(885, 262144, F8, 17) (dual of [262144, 262059, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(861, 262144, F8, 12) (dual of [262144, 262083, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(86, 30, F8, 4) (dual of [30, 24, 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(16) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(891, 262174, F8, 17) (dual of [262174, 262083, 18]-code), using
(91−17, 91, large)-Net in Base 8 — Upper bound on s
There is no (74, 91, large)-net in base 8, because
- 15 times m-reduction [i] would yield (74, 76, large)-net in base 8, but