Best Known (25, 25+6, s)-Nets in Base 9
(25, 25+6, 177149)-Net over F9 — Constructive and digital
Digital (25, 31, 177149)-net over F9, using
- net defined by OOA [i] based on linear OOA(931, 177149, F9, 6, 6) (dual of [(177149, 6), 1062863, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(931, 531447, F9, 6) (dual of [531447, 531416, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(931, 531441, F9, 6) (dual of [531441, 531410, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(925, 531441, F9, 5) (dual of [531441, 531416, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(90, 6, F9, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- OA 3-folding and stacking [i] based on linear OA(931, 531447, F9, 6) (dual of [531447, 531416, 7]-code), using
(25, 25+6, 531447)-Net over F9 — Digital
Digital (25, 31, 531447)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(931, 531447, F9, 6) (dual of [531447, 531416, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(931, 531441, F9, 6) (dual of [531441, 531410, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(925, 531441, F9, 5) (dual of [531441, 531416, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(90, 6, F9, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
(25, 25+6, large)-Net in Base 9 — Upper bound on s
There is no (25, 31, large)-net in base 9, because
- 4 times m-reduction [i] would yield (25, 27, large)-net in base 9, but