Best Known (184, 208, s)-Nets in Base 3
(184, 208, 132860)-Net over F3 — Constructive and digital
Digital (184, 208, 132860)-net over F3, using
- net defined by OOA [i] based on linear OOA(3208, 132860, F3, 24, 24) (dual of [(132860, 24), 3188432, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3208, 1594320, F3, 24) (dual of [1594320, 1594112, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3208, 1594323, F3, 24) (dual of [1594323, 1594115, 25]-code), using
- 1 times truncation [i] based on linear OA(3209, 1594324, F3, 25) (dual of [1594324, 1594115, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3209, 1594324, F3, 25) (dual of [1594324, 1594115, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3208, 1594323, F3, 24) (dual of [1594323, 1594115, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3208, 1594320, F3, 24) (dual of [1594320, 1594112, 25]-code), using
(184, 208, 398580)-Net over F3 — Digital
Digital (184, 208, 398580)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3208, 398580, F3, 4, 24) (dual of [(398580, 4), 1594112, 25]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3208, 1594320, F3, 24) (dual of [1594320, 1594112, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3208, 1594323, F3, 24) (dual of [1594323, 1594115, 25]-code), using
- 1 times truncation [i] based on linear OA(3209, 1594324, F3, 25) (dual of [1594324, 1594115, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3209, 1594324, F3, 25) (dual of [1594324, 1594115, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3208, 1594323, F3, 24) (dual of [1594323, 1594115, 25]-code), using
- OOA 4-folding [i] based on linear OA(3208, 1594320, F3, 24) (dual of [1594320, 1594112, 25]-code), using
(184, 208, large)-Net in Base 3 — Upper bound on s
There is no (184, 208, large)-net in base 3, because
- 22 times m-reduction [i] would yield (184, 186, large)-net in base 3, but