Best Known (59, 76, s)-Nets in Base 9
(59, 76, 7381)-Net over F9 — Constructive and digital
Digital (59, 76, 7381)-net over F9, using
- net defined by OOA [i] based on linear OOA(976, 7381, F9, 17, 17) (dual of [(7381, 17), 125401, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(976, 59049, F9, 17) (dual of [59049, 58973, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(976, 59049, F9, 17) (dual of [59049, 58973, 18]-code), using
(59, 76, 47404)-Net over F9 — Digital
Digital (59, 76, 47404)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(976, 47404, F9, 17) (dual of [47404, 47328, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(976, 59049, F9, 17) (dual of [59049, 58973, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(976, 59049, F9, 17) (dual of [59049, 58973, 18]-code), using
(59, 76, large)-Net in Base 9 — Upper bound on s
There is no (59, 76, large)-net in base 9, because
- 15 times m-reduction [i] would yield (59, 61, large)-net in base 9, but