Best Known (145−21, 145, s)-Nets in Base 9
(145−21, 145, 838860)-Net over F9 — Constructive and digital
Digital (124, 145, 838860)-net over F9, using
- net defined by OOA [i] based on linear OOA(9145, 838860, F9, 21, 21) (dual of [(838860, 21), 17615915, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(9145, 8388601, F9, 21) (dual of [8388601, 8388456, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(9145, large, F9, 21) (dual of [large, large−145, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 916−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(9145, large, F9, 21) (dual of [large, large−145, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(9145, 8388601, F9, 21) (dual of [8388601, 8388456, 22]-code), using
(145−21, 145, large)-Net over F9 — Digital
Digital (124, 145, large)-net over F9, using
(145−21, 145, large)-Net in Base 9 — Upper bound on s
There is no (124, 145, large)-net in base 9, because
- 19 times m-reduction [i] would yield (124, 126, large)-net in base 9, but