Best Known (174, 195, s)-Nets in Base 3
(174, 195, 159442)-Net over F3 — Constructive and digital
Digital (174, 195, 159442)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 10)-net over F3, using
- net from sequence [i] based on digital (3, 9)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 3 and N(F) ≥ 10, using
- net from sequence [i] based on digital (3, 9)-sequence over F3, using
- digital (161, 182, 159432)-net over F3, using
- net defined by OOA [i] based on linear OOA(3182, 159432, F3, 21, 21) (dual of [(159432, 21), 3347890, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3182, 1594321, F3, 21) (dual of [1594321, 1594139, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3182, 1594322, F3, 21) (dual of [1594322, 1594140, 22]-code), using
- 1 times truncation [i] based on linear OA(3183, 1594323, F3, 22) (dual of [1594323, 1594140, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 1 times truncation [i] based on linear OA(3183, 1594323, F3, 22) (dual of [1594323, 1594140, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3182, 1594322, F3, 21) (dual of [1594322, 1594140, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3182, 1594321, F3, 21) (dual of [1594321, 1594139, 22]-code), using
- net defined by OOA [i] based on linear OOA(3182, 159432, F3, 21, 21) (dual of [(159432, 21), 3347890, 22]-NRT-code), using
- digital (3, 13, 10)-net over F3, using
(174, 195, 531462)-Net over F3 — Digital
Digital (174, 195, 531462)-net over F3, using
- 31 times duplication [i] based on digital (173, 194, 531462)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3194, 531462, F3, 3, 21) (dual of [(531462, 3), 1594192, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3194, 1594386, F3, 21) (dual of [1594386, 1594192, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3194, 1594387, F3, 21) (dual of [1594387, 1594193, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,7]) [i] based on
- linear OA(3183, 1594324, F3, 21) (dual of [1594324, 1594141, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(3131, 1594324, F3, 15) (dual of [1594324, 1594193, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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([0,10]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3194, 1594387, F3, 21) (dual of [1594387, 1594193, 22]-code), using
- OOA 3-folding [i] based on linear OA(3194, 1594386, F3, 21) (dual of [1594386, 1594192, 22]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3194, 531462, F3, 3, 21) (dual of [(531462, 3), 1594192, 22]-NRT-code), using
(174, 195, large)-Net in Base 3 — Upper bound on s
There is no (174, 195, large)-net in base 3, because
- 19 times m-reduction [i] would yield (174, 176, large)-net in base 3, but