Best Known (124, 150, s)-Nets in Base 9
(124, 150, 40884)-Net over F9 — Constructive and digital
Digital (124, 150, 40884)-net over F9, using
- net defined by OOA [i] based on linear OOA(9150, 40884, F9, 26, 26) (dual of [(40884, 26), 1062834, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(9150, 531492, F9, 26) (dual of [531492, 531342, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9150, 531494, F9, 26) (dual of [531494, 531344, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] 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]
- linear OA(997, 531441, F9, 19) (dual of [531441, 531344, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(911, 53, F9, 6) (dual of [53, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(911, 80, F9, 6) (dual of [80, 69, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(911, 80, F9, 6) (dual of [80, 69, 7]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(9150, 531494, F9, 26) (dual of [531494, 531344, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(9150, 531492, F9, 26) (dual of [531492, 531342, 27]-code), using
(124, 150, 676081)-Net over F9 — Digital
Digital (124, 150, 676081)-net over F9, using
(124, 150, large)-Net in Base 9 — Upper bound on s
There is no (124, 150, large)-net in base 9, because
- 24 times m-reduction [i] would yield (124, 126, large)-net in base 9, but