Best Known (133−28, 133, s)-Nets in Base 9
(133−28, 133, 4221)-Net over F9 — Constructive and digital
Digital (105, 133, 4221)-net over F9, using
- net defined by OOA [i] based on linear OOA(9133, 4221, F9, 28, 28) (dual of [(4221, 28), 118055, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(9133, 59094, F9, 28) (dual of [59094, 58961, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(9133, 59096, F9, 28) (dual of [59096, 58963, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(19) [i] based on
- linear OA(9121, 59049, F9, 28) (dual of [59049, 58928, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(986, 59049, F9, 20) (dual of [59049, 58963, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(912, 47, F9, 7) (dual of [47, 35, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(912, 67, F9, 7) (dual of [67, 55, 8]-code), using
- construction X applied to Ce(27) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(9133, 59096, F9, 28) (dual of [59096, 58963, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(9133, 59094, F9, 28) (dual of [59094, 58961, 29]-code), using
(133−28, 133, 68538)-Net over F9 — Digital
Digital (105, 133, 68538)-net over F9, using
(133−28, 133, large)-Net in Base 9 — Upper bound on s
There is no (105, 133, large)-net in base 9, because
- 26 times m-reduction [i] would yield (105, 107, large)-net in base 9, but