Best Known (122, 122+27, s)-Nets in Base 9
(122, 122+27, 40882)-Net over F9 — Constructive and digital
Digital (122, 149, 40882)-net over F9, using
- net defined by OOA [i] based on linear OOA(9149, 40882, F9, 27, 27) (dual of [(40882, 27), 1103665, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(9149, 531467, F9, 27) (dual of [531467, 531318, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(9149, 531470, F9, 27) (dual of [531470, 531321, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,11]) [i] 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]
- linear OA(9121, 531442, F9, 23) (dual of [531442, 531321, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 912−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(94, 28, F9, 3) (dual of [28, 24, 4]-code or 28-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(9149, 531470, F9, 27) (dual of [531470, 531321, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(9149, 531467, F9, 27) (dual of [531467, 531318, 28]-code), using
(122, 122+27, 531470)-Net over F9 — Digital
Digital (122, 149, 531470)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9149, 531470, F9, 27) (dual of [531470, 531321, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,11]) [i] 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]
- linear OA(9121, 531442, F9, 23) (dual of [531442, 531321, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 912−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(94, 28, F9, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,9)), using
- construction X applied to C([0,13]) ⊂ C([0,11]) [i] based on
(122, 122+27, large)-Net in Base 9 — Upper bound on s
There is no (122, 149, large)-net in base 9, because
- 25 times m-reduction [i] would yield (122, 124, large)-net in base 9, but