Best Known (197, 221, s)-Nets in Base 3
(197, 221, 132867)-Net over F3 — Constructive and digital
Digital (197, 221, 132867)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- 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
- net defined by OOA [i] based on linear OOA(3208, 132860, F3, 24, 24) (dual of [(132860, 24), 3188432, 25]-NRT-code), using
- digital (1, 13, 7)-net over F3, using
(197, 221, 531462)-Net over F3 — Digital
Digital (197, 221, 531462)-net over F3, using
- 32 times duplication [i] based on digital (195, 219, 531462)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3219, 531462, F3, 3, 24) (dual of [(531462, 3), 1594167, 25]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3219, 1594386, F3, 24) (dual of [1594386, 1594167, 25]-code), using
- 1 times truncation [i] based on linear OA(3220, 1594387, F3, 25) (dual of [1594387, 1594167, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [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]
- linear OA(3157, 1594324, F3, 19) (dual of [1594324, 1594167, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(311, 63, F3, 5) (dual of [63, 52, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- 1 times truncation [i] based on linear OA(3220, 1594387, F3, 25) (dual of [1594387, 1594167, 26]-code), using
- OOA 3-folding [i] based on linear OA(3219, 1594386, F3, 24) (dual of [1594386, 1594167, 25]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3219, 531462, F3, 3, 24) (dual of [(531462, 3), 1594167, 25]-NRT-code), using
(197, 221, large)-Net in Base 3 — Upper bound on s
There is no (197, 221, large)-net in base 3, because
- 22 times m-reduction [i] would yield (197, 199, large)-net in base 3, but