Best Known (94, 121, s)-Nets in Base 9
(94, 121, 4542)-Net over F9 — Constructive and digital
Digital (94, 121, 4542)-net over F9, using
- 91 times duplication [i] based on digital (93, 120, 4542)-net over F9, using
- net defined by OOA [i] based on linear OOA(9120, 4542, F9, 27, 27) (dual of [(4542, 27), 122514, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(9120, 59047, F9, 27) (dual of [59047, 58927, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(9120, 59048, F9, 27) (dual of [59048, 58928, 28]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(9121, 59049, F9, 28) (dual of [59049, 58928, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(9120, 59048, F9, 27) (dual of [59048, 58928, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(9120, 59047, F9, 27) (dual of [59047, 58927, 28]-code), using
- net defined by OOA [i] based on linear OOA(9120, 4542, F9, 27, 27) (dual of [(4542, 27), 122514, 28]-NRT-code), using
(94, 121, 48391)-Net over F9 — Digital
Digital (94, 121, 48391)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9121, 48391, F9, 27) (dual of [48391, 48270, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(9121, 59050, F9, 27) (dual of [59050, 58929, 28]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(9121, 59050, F9, 27) (dual of [59050, 58929, 28]-code), using
(94, 121, large)-Net in Base 9 — Upper bound on s
There is no (94, 121, large)-net in base 9, because
- 25 times m-reduction [i] would yield (94, 96, large)-net in base 9, but