Best Known (117−26, 117, s)-Nets in Base 8
(117−26, 117, 2522)-Net over F8 — Constructive and digital
Digital (91, 117, 2522)-net over F8, using
- 82 times duplication [i] based on digital (89, 115, 2522)-net over F8, using
- net defined by OOA [i] based on linear OOA(8115, 2522, F8, 26, 26) (dual of [(2522, 26), 65457, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(8115, 32786, F8, 26) (dual of [32786, 32671, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8115, 32787, F8, 26) (dual of [32787, 32672, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- 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(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(84, 19, F8, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,8)), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(8115, 32787, F8, 26) (dual of [32787, 32672, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(8115, 32786, F8, 26) (dual of [32786, 32671, 27]-code), using
- net defined by OOA [i] based on linear OOA(8115, 2522, F8, 26, 26) (dual of [(2522, 26), 65457, 27]-NRT-code), using
(117−26, 117, 32434)-Net over F8 — Digital
Digital (91, 117, 32434)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8117, 32434, F8, 26) (dual of [32434, 32317, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8117, 32794, F8, 26) (dual of [32794, 32677, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- 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(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(86, 26, F8, 4) (dual of [26, 20, 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(25) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(8117, 32794, F8, 26) (dual of [32794, 32677, 27]-code), using
(117−26, 117, large)-Net in Base 8 — Upper bound on s
There is no (91, 117, large)-net in base 8, because
- 24 times m-reduction [i] would yield (91, 93, large)-net in base 8, but