Best Known (25, 34, s)-Nets in Base 9
(25, 34, 3281)-Net over F9 — Constructive and digital
Digital (25, 34, 3281)-net over F9, using
- net defined by OOA [i] based on linear OOA(934, 3281, F9, 9, 9) (dual of [(3281, 9), 29495, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(934, 13125, F9, 9) (dual of [13125, 13091, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(934, 13126, F9, 9) (dual of [13126, 13092, 10]-code), using
- trace code [i] based on linear OA(8117, 6563, F81, 9) (dual of [6563, 6546, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(8117, 6561, F81, 9) (dual of [6561, 6544, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(8115, 6561, F81, 8) (dual of [6561, 6546, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- trace code [i] based on linear OA(8117, 6563, F81, 9) (dual of [6563, 6546, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(934, 13126, F9, 9) (dual of [13126, 13092, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(934, 13125, F9, 9) (dual of [13125, 13091, 10]-code), using
(25, 34, 13126)-Net over F9 — Digital
Digital (25, 34, 13126)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(934, 13126, F9, 9) (dual of [13126, 13092, 10]-code), using
- trace code [i] based on linear OA(8117, 6563, F81, 9) (dual of [6563, 6546, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(8117, 6561, F81, 9) (dual of [6561, 6544, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(8115, 6561, F81, 8) (dual of [6561, 6546, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- trace code [i] based on linear OA(8117, 6563, F81, 9) (dual of [6563, 6546, 10]-code), using
(25, 34, large)-Net in Base 9 — Upper bound on s
There is no (25, 34, large)-net in base 9, because
- 7 times m-reduction [i] would yield (25, 27, large)-net in base 9, but