Best Known (93, 117, s)-Nets in Base 9
(93, 117, 4924)-Net over F9 — Constructive and digital
Digital (93, 117, 4924)-net over F9, using
- 91 times duplication [i] based on digital (92, 116, 4924)-net over F9, using
- net defined by OOA [i] based on linear OOA(9116, 4924, F9, 24, 24) (dual of [(4924, 24), 118060, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(9116, 59088, F9, 24) (dual of [59088, 58972, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(9116, 59089, F9, 24) (dual of [59089, 58973, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- linear OA(9106, 59049, F9, 24) (dual of [59049, 58943, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(976, 59049, F9, 17) (dual of [59049, 58973, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(910, 40, F9, 6) (dual of [40, 30, 7]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 40 | 92−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(9116, 59089, F9, 24) (dual of [59089, 58973, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(9116, 59088, F9, 24) (dual of [59088, 58972, 25]-code), using
- net defined by OOA [i] based on linear OOA(9116, 4924, F9, 24, 24) (dual of [(4924, 24), 118060, 25]-NRT-code), using
(93, 117, 84259)-Net over F9 — Digital
Digital (93, 117, 84259)-net over F9, using
(93, 117, large)-Net in Base 9 — Upper bound on s
There is no (93, 117, large)-net in base 9, because
- 22 times m-reduction [i] would yield (93, 95, large)-net in base 9, but