Best Known (60−14, 60, s)-Nets in Base 9
(60−14, 60, 1877)-Net over F9 — Constructive and digital
Digital (46, 60, 1877)-net over F9, using
- 91 times duplication [i] based on digital (45, 59, 1877)-net over F9, using
- net defined by OOA [i] based on linear OOA(959, 1877, F9, 14, 14) (dual of [(1877, 14), 26219, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(959, 13139, F9, 14) (dual of [13139, 13080, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(958, 13138, F9, 14) (dual of [13138, 13080, 15]-code), using
- trace code [i] based on linear OA(8129, 6569, F81, 14) (dual of [6569, 6540, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(8121, 6561, F81, 11) (dual of [6561, 6540, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(812, 8, F81, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,81)), using
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- Reed–Solomon code RS(79,81) [i]
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- trace code [i] based on linear OA(8129, 6569, F81, 14) (dual of [6569, 6540, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(958, 13138, F9, 14) (dual of [13138, 13080, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(959, 13139, F9, 14) (dual of [13139, 13080, 15]-code), using
- net defined by OOA [i] based on linear OOA(959, 1877, F9, 14, 14) (dual of [(1877, 14), 26219, 15]-NRT-code), using
(60−14, 60, 2812)-Net in Base 9 — Constructive
(46, 60, 2812)-net in base 9, using
- base change [i] based on digital (26, 40, 2812)-net over F27, using
- net defined by OOA [i] based on linear OOA(2740, 2812, F27, 14, 14) (dual of [(2812, 14), 39328, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2740, 19684, F27, 14) (dual of [19684, 19644, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2740, 19686, F27, 14) (dual of [19686, 19646, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(2740, 19683, F27, 14) (dual of [19683, 19643, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2737, 19683, F27, 13) (dual of [19683, 19646, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(2740, 19686, F27, 14) (dual of [19686, 19646, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2740, 19684, F27, 14) (dual of [19684, 19644, 15]-code), using
- net defined by OOA [i] based on linear OOA(2740, 2812, F27, 14, 14) (dual of [(2812, 14), 39328, 15]-NRT-code), using
(60−14, 60, 17975)-Net over F9 — Digital
Digital (46, 60, 17975)-net over F9, using
(60−14, 60, large)-Net in Base 9 — Upper bound on s
There is no (46, 60, large)-net in base 9, because
- 12 times m-reduction [i] would yield (46, 48, large)-net in base 9, but