Best Known (118, 118+27, s)-Nets in Base 9
(118, 118+27, 40880)-Net over F9 — Constructive and digital
Digital (118, 145, 40880)-net over F9, using
- net defined by OOA [i] based on linear OOA(9145, 40880, F9, 27, 27) (dual of [(40880, 27), 1103615, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(9145, 531441, F9, 27) (dual of [531441, 531296, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(9145, 531442, F9, 27) (dual of [531442, 531297, 28]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 531442 | 912−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(9145, 531442, F9, 27) (dual of [531442, 531297, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(9145, 531441, F9, 27) (dual of [531441, 531296, 28]-code), using
(118, 118+27, 398985)-Net over F9 — Digital
Digital (118, 145, 398985)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9145, 398985, F9, 27) (dual of [398985, 398840, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(9145, 531442, F9, 27) (dual of [531442, 531297, 28]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 531442 | 912−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(9145, 531442, F9, 27) (dual of [531442, 531297, 28]-code), using
(118, 118+27, large)-Net in Base 9 — Upper bound on s
There is no (118, 145, large)-net in base 9, because
- 25 times m-reduction [i] would yield (118, 120, large)-net in base 9, but