Best Known (96−23, 96, s)-Nets in Base 27
(96−23, 96, 48315)-Net over F27 — Constructive and digital
Digital (73, 96, 48315)-net over F27, using
- 272 times duplication [i] based on digital (71, 94, 48315)-net over F27, using
- net defined by OOA [i] based on linear OOA(2794, 48315, F27, 23, 23) (dual of [(48315, 23), 1111151, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2794, 531466, F27, 23) (dual of [531466, 531372, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2794, 531470, F27, 23) (dual of [531470, 531376, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,8]) [i] based on
- linear OA(2789, 531442, F27, 23) (dual of [531442, 531353, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(2765, 531442, F27, 17) (dual of [531442, 531377, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(275, 28, F27, 5) (dual of [28, 23, 6]-code or 28-arc in PG(4,27)), using
- extended Reed–Solomon code RSe(23,27) [i]
- the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- construction X applied to C([0,11]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2794, 531470, F27, 23) (dual of [531470, 531376, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2794, 531466, F27, 23) (dual of [531466, 531372, 24]-code), using
- net defined by OOA [i] based on linear OOA(2794, 48315, F27, 23, 23) (dual of [(48315, 23), 1111151, 24]-NRT-code), using
(96−23, 96, 613534)-Net over F27 — Digital
Digital (73, 96, 613534)-net over F27, using
(96−23, 96, large)-Net in Base 27 — Upper bound on s
There is no (73, 96, large)-net in base 27, because
- 21 times m-reduction [i] would yield (73, 75, large)-net in base 27, but