Best Known (172, 172+22, s)-Nets in Base 3
(172, 172+22, 144944)-Net over F3 — Constructive and digital
Digital (172, 194, 144944)-net over F3, using
- net defined by OOA [i] based on linear OOA(3194, 144944, F3, 22, 22) (dual of [(144944, 22), 3188574, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3194, 1594384, F3, 22) (dual of [1594384, 1594190, 23]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(3194, 1594386, F3, 22) (dual of [1594386, 1594192, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3194, 1594384, F3, 22) (dual of [1594384, 1594190, 23]-code), using
(172, 172+22, 436385)-Net over F3 — Digital
Digital (172, 194, 436385)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3194, 436385, F3, 3, 22) (dual of [(436385, 3), 1308961, 23]-NRT-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OOA(3194, 531462, F3, 3, 22) (dual of [(531462, 3), 1594192, 23]-NRT-code), using
(172, 172+22, large)-Net in Base 3 — Upper bound on s
There is no (172, 194, large)-net in base 3, because
- 20 times m-reduction [i] would yield (172, 174, large)-net in base 3, but