Best Known (85, 113, s)-Nets in Base 9
(85, 113, 938)-Net over F9 — Constructive and digital
Digital (85, 113, 938)-net over F9, using
- 91 times duplication [i] based on digital (84, 112, 938)-net over F9, using
- net defined by OOA [i] based on linear OOA(9112, 938, F9, 28, 28) (dual of [(938, 28), 26152, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(9112, 13132, F9, 28) (dual of [13132, 13020, 29]-code), using
- trace code [i] based on linear OA(8156, 6566, F81, 28) (dual of [6566, 6510, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(8155, 6561, F81, 28) (dual of [6561, 6506, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8151, 6561, F81, 26) (dual of [6561, 6510, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- trace code [i] based on linear OA(8156, 6566, F81, 28) (dual of [6566, 6510, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(9112, 13132, F9, 28) (dual of [13132, 13020, 29]-code), using
- net defined by OOA [i] based on linear OOA(9112, 938, F9, 28, 28) (dual of [(938, 28), 26152, 29]-NRT-code), using
(85, 113, 13472)-Net over F9 — Digital
Digital (85, 113, 13472)-net over F9, using
(85, 113, large)-Net in Base 9 — Upper bound on s
There is no (85, 113, large)-net in base 9, because
- 26 times m-reduction [i] would yield (85, 87, large)-net in base 9, but