Best Known (115−22, 115, s)-Nets in Base 9
(115−22, 115, 48313)-Net over F9 — Constructive and digital
Digital (93, 115, 48313)-net over F9, using
- net defined by OOA [i] based on linear OOA(9115, 48313, F9, 22, 22) (dual of [(48313, 22), 1062771, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(9115, 531443, F9, 22) (dual of [531443, 531328, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(9115, 531447, F9, 22) (dual of [531447, 531332, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(9115, 531441, F9, 22) (dual of [531441, 531326, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(9109, 531441, F9, 21) (dual of [531441, 531332, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(9115, 531447, F9, 22) (dual of [531447, 531332, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(9115, 531443, F9, 22) (dual of [531443, 531328, 23]-code), using
(115−22, 115, 285352)-Net over F9 — Digital
Digital (93, 115, 285352)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9115, 285352, F9, 22) (dual of [285352, 285237, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(9115, 531441, F9, 22) (dual of [531441, 531326, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(9115, 531441, F9, 22) (dual of [531441, 531326, 23]-code), using
(115−22, 115, large)-Net in Base 9 — Upper bound on s
There is no (93, 115, large)-net in base 9, because
- 20 times m-reduction [i] would yield (93, 95, large)-net in base 9, but