Best Known (74, 74+22, s)-Nets in Base 9
(74, 74+22, 5368)-Net over F9 — Constructive and digital
Digital (74, 96, 5368)-net over F9, using
- net defined by OOA [i] based on linear OOA(996, 5368, F9, 22, 22) (dual of [(5368, 22), 118000, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(996, 59048, F9, 22) (dual of [59048, 58952, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(996, 59049, F9, 22) (dual of [59049, 58953, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(996, 59049, F9, 22) (dual of [59049, 58953, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(996, 59048, F9, 22) (dual of [59048, 58952, 23]-code), using
(74, 74+22, 35378)-Net over F9 — Digital
Digital (74, 96, 35378)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(996, 35378, F9, 22) (dual of [35378, 35282, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(996, 59049, F9, 22) (dual of [59049, 58953, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(996, 59049, F9, 22) (dual of [59049, 58953, 23]-code), using
(74, 74+22, large)-Net in Base 9 — Upper bound on s
There is no (74, 96, large)-net in base 9, because
- 20 times m-reduction [i] would yield (74, 76, large)-net in base 9, but