Best Known (95−21, 95, s)-Nets in Base 8
(95−21, 95, 3279)-Net over F8 — Constructive and digital
Digital (74, 95, 3279)-net over F8, using
- net defined by OOA [i] based on linear OOA(895, 3279, F8, 21, 21) (dual of [(3279, 21), 68764, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(895, 32791, F8, 21) (dual of [32791, 32696, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(895, 32793, F8, 21) (dual of [32793, 32698, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(891, 32769, F8, 21) (dual of [32769, 32678, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(871, 32769, F8, 17) (dual of [32769, 32698, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(84, 24, F8, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,8)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(895, 32793, F8, 21) (dual of [32793, 32698, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(895, 32791, F8, 21) (dual of [32791, 32696, 22]-code), using
(95−21, 95, 32793)-Net over F8 — Digital
Digital (74, 95, 32793)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(895, 32793, F8, 21) (dual of [32793, 32698, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(891, 32769, F8, 21) (dual of [32769, 32678, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(871, 32769, F8, 17) (dual of [32769, 32698, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(84, 24, F8, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,8)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
(95−21, 95, large)-Net in Base 8 — Upper bound on s
There is no (74, 95, large)-net in base 8, because
- 19 times m-reduction [i] would yield (74, 76, large)-net in base 8, but