Best Known (96, 115, s)-Nets in Base 8
(96, 115, 233018)-Net over F8 — Constructive and digital
Digital (96, 115, 233018)-net over F8, using
- 81 times duplication [i] based on digital (95, 114, 233018)-net over F8, using
- net defined by OOA [i] based on linear OOA(8114, 233018, F8, 19, 19) (dual of [(233018, 19), 4427228, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8114, 2097163, F8, 19) (dual of [2097163, 2097049, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8114, 2097168, F8, 19) (dual of [2097168, 2097054, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(8113, 2097153, F8, 19) (dual of [2097153, 2097040, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8114, 2097168, F8, 19) (dual of [2097168, 2097054, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8114, 2097163, F8, 19) (dual of [2097163, 2097049, 20]-code), using
- net defined by OOA [i] based on linear OOA(8114, 233018, F8, 19, 19) (dual of [(233018, 19), 4427228, 20]-NRT-code), using
(96, 115, 1166430)-Net over F8 — Digital
Digital (96, 115, 1166430)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8115, 1166430, F8, 19) (dual of [1166430, 1166315, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8115, 2097169, F8, 19) (dual of [2097169, 2097054, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8114, 2097168, F8, 19) (dual of [2097168, 2097054, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(8113, 2097153, F8, 19) (dual of [2097153, 2097040, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(8114, 2097168, F8, 19) (dual of [2097168, 2097054, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8115, 2097169, F8, 19) (dual of [2097169, 2097054, 20]-code), using
(96, 115, large)-Net in Base 8 — Upper bound on s
There is no (96, 115, large)-net in base 8, because
- 17 times m-reduction [i] would yield (96, 98, large)-net in base 8, but