Best Known (135−19, 135, s)-Nets in Base 8
(135−19, 135, 932067)-Net over F8 — Constructive and digital
Digital (116, 135, 932067)-net over F8, using
- 83 times duplication [i] based on digital (113, 132, 932067)-net over F8, using
- net defined by OOA [i] based on linear OOA(8132, 932067, F8, 21, 19) (dual of [(932067, 21), 19573275, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8132, 2796202, F8, 3, 19) (dual of [(2796202, 3), 8388474, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8129, 2796201, F8, 3, 19) (dual of [(2796201, 3), 8388474, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8129, large, F8, 19) (dual of [large, large−129, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 816−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(8129, large, F8, 19) (dual of [large, large−129, 20]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8129, 2796201, F8, 3, 19) (dual of [(2796201, 3), 8388474, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8132, 2796202, F8, 3, 19) (dual of [(2796202, 3), 8388474, 20]-NRT-code), using
- net defined by OOA [i] based on linear OOA(8132, 932067, F8, 21, 19) (dual of [(932067, 21), 19573275, 20]-NRT-code), using
(135−19, 135, large)-Net over F8 — Digital
Digital (116, 135, large)-net over F8, using
- 83 times duplication [i] based on digital (113, 132, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8132, large, F8, 19) (dual of [large, large−132, 20]-code), using
- 3 times code embedding in larger space [i] based on linear OA(8129, large, F8, 19) (dual of [large, large−129, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 816−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 3 times code embedding in larger space [i] based on linear OA(8129, large, F8, 19) (dual of [large, large−129, 20]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8132, large, F8, 19) (dual of [large, large−132, 20]-code), using
(135−19, 135, large)-Net in Base 8 — Upper bound on s
There is no (116, 135, large)-net in base 8, because
- 17 times m-reduction [i] would yield (116, 118, large)-net in base 8, but