Best Known (93, 121, s)-Nets in Base 9
(93, 121, 4217)-Net over F9 — Constructive and digital
Digital (93, 121, 4217)-net over F9, using
- net defined by OOA [i] based on linear OOA(9121, 4217, F9, 28, 28) (dual of [(4217, 28), 117955, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(9121, 59038, F9, 28) (dual of [59038, 58917, 29]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(9121, 59049, F9, 28) (dual of [59049, 58928, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(9121, 59038, F9, 28) (dual of [59038, 58917, 29]-code), using
(93, 121, 33435)-Net over F9 — Digital
Digital (93, 121, 33435)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9121, 33435, F9, 28) (dual of [33435, 33314, 29]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(9121, 59049, F9, 28) (dual of [59049, 58928, 29]-code), using
(93, 121, large)-Net in Base 9 — Upper bound on s
There is no (93, 121, large)-net in base 9, because
- 26 times m-reduction [i] would yield (93, 95, large)-net in base 9, but