Best Known (158, 180, s)-Nets in Base 3
(158, 180, 48318)-Net over F3 — Constructive and digital
Digital (158, 180, 48318)-net over F3, using
- net defined by OOA [i] based on linear OOA(3180, 48318, F3, 22, 22) (dual of [(48318, 22), 1062816, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3180, 531498, F3, 22) (dual of [531498, 531318, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3180, 531500, F3, 22) (dual of [531500, 531320, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(311, 59, F3, 5) (dual of [59, 48, 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(3180, 531500, F3, 22) (dual of [531500, 531320, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3180, 531498, F3, 22) (dual of [531498, 531318, 23]-code), using
(158, 180, 177166)-Net over F3 — Digital
Digital (158, 180, 177166)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3180, 177166, F3, 3, 22) (dual of [(177166, 3), 531318, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3180, 531498, F3, 22) (dual of [531498, 531318, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3180, 531500, F3, 22) (dual of [531500, 531320, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(311, 59, F3, 5) (dual of [59, 48, 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(3180, 531500, F3, 22) (dual of [531500, 531320, 23]-code), using
- OOA 3-folding [i] based on linear OA(3180, 531498, F3, 22) (dual of [531498, 531318, 23]-code), using
(158, 180, large)-Net in Base 3 — Upper bound on s
There is no (158, 180, large)-net in base 3, because
- 20 times m-reduction [i] would yield (158, 160, large)-net in base 3, but