Best Known (125−17, 125, s)-Nets in Base 9
(125−17, 125, 1048575)-Net over F9 — Constructive and digital
Digital (108, 125, 1048575)-net over F9, using
- 94 times duplication [i] based on digital (104, 121, 1048575)-net over F9, using
- net defined by OOA [i] based on linear OOA(9121, 1048575, F9, 17, 17) (dual of [(1048575, 17), 17825654, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(9121, 8388601, F9, 17) (dual of [8388601, 8388480, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(9121, large, F9, 17) (dual of [large, large−121, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(9121, large, F9, 17) (dual of [large, large−121, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(9121, 8388601, F9, 17) (dual of [8388601, 8388480, 18]-code), using
- net defined by OOA [i] based on linear OOA(9121, 1048575, F9, 17, 17) (dual of [(1048575, 17), 17825654, 18]-NRT-code), using
(125−17, 125, large)-Net over F9 — Digital
Digital (108, 125, large)-net over F9, using
- t-expansion [i] based on digital (107, 125, large)-net over F9, using
(125−17, 125, large)-Net in Base 9 — Upper bound on s
There is no (108, 125, large)-net in base 9, because
- 15 times m-reduction [i] would yield (108, 110, large)-net in base 9, but