Best Known (117, 145, s)-Nets in Base 9
(117, 145, 37960)-Net over F9 — Constructive and digital
Digital (117, 145, 37960)-net over F9, using
- net defined by OOA [i] based on linear OOA(9145, 37960, F9, 28, 28) (dual of [(37960, 28), 1062735, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(9145, 531440, F9, 28) (dual of [531440, 531295, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(9145, 531441, F9, 28) (dual of [531441, 531296, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(9145, 531441, F9, 28) (dual of [531441, 531296, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(9145, 531440, F9, 28) (dual of [531440, 531295, 29]-code), using
(117, 145, 265720)-Net over F9 — Digital
Digital (117, 145, 265720)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(9145, 265720, F9, 2, 28) (dual of [(265720, 2), 531295, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9145, 531440, F9, 28) (dual of [531440, 531295, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(9145, 531441, F9, 28) (dual of [531441, 531296, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(9145, 531441, F9, 28) (dual of [531441, 531296, 29]-code), using
- OOA 2-folding [i] based on linear OA(9145, 531440, F9, 28) (dual of [531440, 531295, 29]-code), using
(117, 145, large)-Net in Base 9 — Upper bound on s
There is no (117, 145, large)-net in base 9, because
- 26 times m-reduction [i] would yield (117, 119, large)-net in base 9, but