Best Known (115, 115+30, s)-Nets in Base 8
(115, 115+30, 2188)-Net over F8 — Constructive and digital
Digital (115, 145, 2188)-net over F8, using
- net defined by OOA [i] based on linear OOA(8145, 2188, F8, 30, 30) (dual of [(2188, 30), 65495, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(8145, 32820, F8, 30) (dual of [32820, 32675, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(8145, 32822, F8, 30) (dual of [32822, 32677, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(20) [i] based on
- linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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(814, 54, F8, 8) (dual of [54, 40, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(814, 63, F8, 8) (dual of [63, 49, 9]-code), using
- construction X applied to Ce(29) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(8145, 32822, F8, 30) (dual of [32822, 32677, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(8145, 32820, F8, 30) (dual of [32820, 32675, 31]-code), using
(115, 115+30, 54650)-Net over F8 — Digital
Digital (115, 145, 54650)-net over F8, using
(115, 115+30, large)-Net in Base 8 — Upper bound on s
There is no (115, 145, large)-net in base 8, because
- 28 times m-reduction [i] would yield (115, 117, large)-net in base 8, but