Best Known (128−26, 128, s)-Nets in Base 9
(128−26, 128, 4545)-Net over F9 — Constructive and digital
Digital (102, 128, 4545)-net over F9, using
- t-expansion [i] based on digital (101, 128, 4545)-net over F9, using
- net defined by OOA [i] based on linear OOA(9128, 4545, F9, 27, 27) (dual of [(4545, 27), 122587, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(9128, 59086, F9, 27) (dual of [59086, 58958, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(9128, 59087, F9, 27) (dual of [59087, 58959, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,10]) [i] based on
- linear OA(9121, 59050, F9, 27) (dual of [59050, 58929, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(991, 59050, F9, 21) (dual of [59050, 58959, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(97, 37, F9, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- construction X applied to C([0,13]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(9128, 59087, F9, 27) (dual of [59087, 58959, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(9128, 59086, F9, 27) (dual of [59086, 58958, 28]-code), using
- net defined by OOA [i] based on linear OOA(9128, 4545, F9, 27, 27) (dual of [(4545, 27), 122587, 28]-NRT-code), using
(128−26, 128, 97794)-Net over F9 — Digital
Digital (102, 128, 97794)-net over F9, using
(128−26, 128, large)-Net in Base 9 — Upper bound on s
There is no (102, 128, large)-net in base 9, because
- 24 times m-reduction [i] would yield (102, 104, large)-net in base 9, but