Best Known (139−26, 139, s)-Nets in Base 9
(139−26, 139, 40880)-Net over F9 — Constructive and digital
Digital (113, 139, 40880)-net over F9, using
- net defined by OOA [i] based on linear OOA(9139, 40880, F9, 26, 26) (dual of [(40880, 26), 1062741, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(9139, 531440, F9, 26) (dual of [531440, 531301, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9139, 531441, F9, 26) (dual of [531441, 531302, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(9139, 531441, F9, 26) (dual of [531441, 531302, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(9139, 531440, F9, 26) (dual of [531440, 531301, 27]-code), using
(139−26, 139, 375968)-Net over F9 — Digital
Digital (113, 139, 375968)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9139, 375968, F9, 26) (dual of [375968, 375829, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9139, 531441, F9, 26) (dual of [531441, 531302, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(9139, 531441, F9, 26) (dual of [531441, 531302, 27]-code), using
(139−26, 139, large)-Net in Base 9 — Upper bound on s
There is no (113, 139, large)-net in base 9, because
- 24 times m-reduction [i] would yield (113, 115, large)-net in base 9, but