Best Known (92, 92+12, s)-Nets in Base 3
(92, 92+12, 265720)-Net over F3 — Constructive and digital
Digital (92, 104, 265720)-net over F3, using
- net defined by OOA [i] based on linear OOA(3104, 265720, F3, 12, 12) (dual of [(265720, 12), 3188536, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3104, 1594320, F3, 12) (dual of [1594320, 1594216, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3104, 1594322, F3, 12) (dual of [1594322, 1594218, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(3104, 1594322, F3, 12) (dual of [1594322, 1594218, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(3104, 1594320, F3, 12) (dual of [1594320, 1594216, 13]-code), using
(92, 92+12, 531441)-Net over F3 — Digital
Digital (92, 104, 531441)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3104, 531441, F3, 3, 12) (dual of [(531441, 3), 1594219, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3104, 1594323, F3, 12) (dual of [1594323, 1594219, 13]-code), using
- 1 times truncation [i] based on linear OA(3105, 1594324, F3, 13) (dual of [1594324, 1594219, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3105, 1594324, F3, 13) (dual of [1594324, 1594219, 14]-code), using
- OOA 3-folding [i] based on linear OA(3104, 1594323, F3, 12) (dual of [1594323, 1594219, 13]-code), using
(92, 92+12, large)-Net in Base 3 — Upper bound on s
There is no (92, 104, large)-net in base 3, because
- 10 times m-reduction [i] would yield (92, 94, large)-net in base 3, but