Best Known (98, 98+27, s)-Nets in Base 9
(98, 98+27, 4544)-Net over F9 — Constructive and digital
Digital (98, 125, 4544)-net over F9, using
- net defined by OOA [i] based on linear OOA(9125, 4544, F9, 27, 27) (dual of [(4544, 27), 122563, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(9125, 59073, F9, 27) (dual of [59073, 58948, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(9125, 59074, F9, 27) (dual of [59074, 58949, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,11]) [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(9101, 59050, F9, 23) (dual of [59050, 58949, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(94, 24, F9, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,9)), using
- construction X applied to C([0,13]) ⊂ C([0,11]) [i] based on
- discarding factors / shortening the dual code based on linear OA(9125, 59074, F9, 27) (dual of [59074, 58949, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(9125, 59073, F9, 27) (dual of [59073, 58948, 28]-code), using
(98, 98+27, 59074)-Net over F9 — Digital
Digital (98, 125, 59074)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9125, 59074, F9, 27) (dual of [59074, 58949, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,11]) [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(9101, 59050, F9, 23) (dual of [59050, 58949, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(94, 24, F9, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,9)), using
- construction X applied to C([0,13]) ⊂ C([0,11]) [i] based on
(98, 98+27, large)-Net in Base 9 — Upper bound on s
There is no (98, 125, large)-net in base 9, because
- 25 times m-reduction [i] would yield (98, 100, large)-net in base 9, but