Best Known (35, 49, s)-Nets in Base 9
(35, 49, 937)-Net over F9 — Constructive and digital
Digital (35, 49, 937)-net over F9, using
- net defined by OOA [i] based on linear OOA(949, 937, F9, 14, 14) (dual of [(937, 14), 13069, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(949, 6559, F9, 14) (dual of [6559, 6510, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(949, 6561, F9, 14) (dual of [6561, 6512, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(949, 6561, F9, 14) (dual of [6561, 6512, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(949, 6559, F9, 14) (dual of [6559, 6510, 15]-code), using
(35, 49, 4331)-Net over F9 — Digital
Digital (35, 49, 4331)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(949, 4331, F9, 14) (dual of [4331, 4282, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(949, 6561, F9, 14) (dual of [6561, 6512, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(949, 6561, F9, 14) (dual of [6561, 6512, 15]-code), using
(35, 49, 2020809)-Net in Base 9 — Upper bound on s
There is no (35, 49, 2020810)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 57264 250156 109850 126397 151231 936842 635639 428337 > 949 [i]