Best Known (46, 64, s)-Nets in Base 9
(46, 64, 729)-Net over F9 — Constructive and digital
Digital (46, 64, 729)-net over F9, using
- net defined by OOA [i] based on linear OOA(964, 729, F9, 18, 18) (dual of [(729, 18), 13058, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(964, 6561, F9, 18) (dual of [6561, 6497, 19]-code), using
- 1 times truncation [i] based on linear OA(965, 6562, F9, 19) (dual of [6562, 6497, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(965, 6562, F9, 19) (dual of [6562, 6497, 20]-code), using
- OA 9-folding and stacking [i] based on linear OA(964, 6561, F9, 18) (dual of [6561, 6497, 19]-code), using
(46, 64, 4853)-Net over F9 — Digital
Digital (46, 64, 4853)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(964, 4853, F9, 18) (dual of [4853, 4789, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(964, 6561, F9, 18) (dual of [6561, 6497, 19]-code), using
- 1 times truncation [i] based on linear OA(965, 6562, F9, 19) (dual of [6562, 6497, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(965, 6562, F9, 19) (dual of [6562, 6497, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(964, 6561, F9, 18) (dual of [6561, 6497, 19]-code), using
(46, 64, 3165084)-Net in Base 9 — Upper bound on s
There is no (46, 64, 3165085)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 11 790211 029368 855271 939822 408735 003403 023937 231295 647676 802857 > 964 [i]