Best Known (25, 25+10, s)-Nets in Base 9
(25, 25+10, 1314)-Net over F9 — Constructive and digital
Digital (25, 35, 1314)-net over F9, using
- net defined by OOA [i] based on linear OOA(935, 1314, F9, 10, 10) (dual of [(1314, 10), 13105, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(935, 6570, F9, 10) (dual of [6570, 6535, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(935, 6571, F9, 10) (dual of [6571, 6536, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(933, 6561, F9, 10) (dual of [6561, 6528, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(925, 6561, F9, 7) (dual of [6561, 6536, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(92, 10, F9, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,9)), using
- extended Reed–Solomon code RSe(8,9) [i]
- Hamming code H(2,9) [i]
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(935, 6571, F9, 10) (dual of [6571, 6536, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(935, 6570, F9, 10) (dual of [6570, 6535, 11]-code), using
(25, 25+10, 5343)-Net over F9 — Digital
Digital (25, 35, 5343)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(935, 5343, F9, 10) (dual of [5343, 5308, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(935, 6571, F9, 10) (dual of [6571, 6536, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(933, 6561, F9, 10) (dual of [6561, 6528, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(925, 6561, F9, 7) (dual of [6561, 6536, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(92, 10, F9, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,9)), using
- extended Reed–Solomon code RSe(8,9) [i]
- Hamming code H(2,9) [i]
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(935, 6571, F9, 10) (dual of [6571, 6536, 11]-code), using
(25, 25+10, 1557553)-Net in Base 9 — Upper bound on s
There is no (25, 35, 1557554)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 2503 155969 229226 112981 504989 952849 > 935 [i]