Best Known (55, 55+9, s)-Nets in Base 9
(55, 55+9, 2097150)-Net over F9 — Constructive and digital
Digital (55, 64, 2097150)-net over F9, using
- net defined by OOA [i] based on linear OOA(964, 2097150, F9, 9, 9) (dual of [(2097150, 9), 18874286, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(964, 8388601, F9, 9) (dual of [8388601, 8388537, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(964, large, F9, 9) (dual of [large, large−64, 10]-code), using
- the narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(964, large, F9, 9) (dual of [large, large−64, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(964, 8388601, F9, 9) (dual of [8388601, 8388537, 10]-code), using
(55, 55+9, large)-Net over F9 — Digital
Digital (55, 64, large)-net over F9, using
- 1 times m-reduction [i] based on digital (55, 65, large)-net over F9, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(965, large, F9, 10) (dual of [large, large−65, 11]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(965, large, F9, 10) (dual of [large, large−65, 11]-code), using
(55, 55+9, large)-Net in Base 9 — Upper bound on s
There is no (55, 64, large)-net in base 9, because
- 7 times m-reduction [i] would yield (55, 57, large)-net in base 9, but