Best Known (173, 195, s)-Nets in Base 3
(173, 195, 144945)-Net over F3 — Constructive and digital
Digital (173, 195, 144945)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 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 (161, 183, 144938)-net over F3, using
- net defined by OOA [i] based on linear OOA(3183, 144938, F3, 22, 22) (dual of [(144938, 22), 3188453, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3183, 1594318, F3, 22) (dual of [1594318, 1594135, 23]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(3183, 1594323, F3, 22) (dual of [1594323, 1594140, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3183, 1594318, F3, 22) (dual of [1594318, 1594135, 23]-code), using
- net defined by OOA [i] based on linear OOA(3183, 144938, F3, 22, 22) (dual of [(144938, 22), 3188453, 23]-NRT-code), using
- digital (1, 12, 7)-net over F3, using
(173, 195, 463850)-Net over F3 — Digital
Digital (173, 195, 463850)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3195, 463850, F3, 3, 22) (dual of [(463850, 3), 1391355, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3195, 531462, F3, 3, 22) (dual of [(531462, 3), 1594191, 23]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3194, 531462, F3, 3, 22) (dual of [(531462, 3), 1594192, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3194, 1594386, F3, 22) (dual of [1594386, 1594192, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [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]
- linear OA(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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 Ce(21) ⊂ Ce(15) [i] based on
- OOA 3-folding [i] based on linear OA(3194, 1594386, F3, 22) (dual of [1594386, 1594192, 23]-code), using
- 31 times duplication [i] based on linear OOA(3194, 531462, F3, 3, 22) (dual of [(531462, 3), 1594192, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3195, 531462, F3, 3, 22) (dual of [(531462, 3), 1594191, 23]-NRT-code), using
(173, 195, large)-Net in Base 3 — Upper bound on s
There is no (173, 195, large)-net in base 3, because
- 20 times m-reduction [i] would yield (173, 175, large)-net in base 3, but