Best Known (113, 127, s)-Nets in Base 3
(113, 127, 683283)-Net over F3 — Constructive and digital
Digital (113, 127, 683283)-net over F3, using
- net defined by OOA [i] based on linear OOA(3127, 683283, F3, 14, 14) (dual of [(683283, 14), 9565835, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3127, 4782981, F3, 14) (dual of [4782981, 4782854, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3127, 4782983, F3, 14) (dual of [4782983, 4782856, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(3127, 4782969, F3, 14) (dual of [4782969, 4782842, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3127, 4782983, F3, 14) (dual of [4782983, 4782856, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3127, 4782981, F3, 14) (dual of [4782981, 4782854, 15]-code), using
(113, 127, 1594327)-Net over F3 — Digital
Digital (113, 127, 1594327)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3127, 1594327, F3, 3, 14) (dual of [(1594327, 3), 4782854, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3127, 4782981, F3, 14) (dual of [4782981, 4782854, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3127, 4782983, F3, 14) (dual of [4782983, 4782856, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(3127, 4782969, F3, 14) (dual of [4782969, 4782842, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3113, 4782969, F3, 13) (dual of [4782969, 4782856, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3127, 4782983, F3, 14) (dual of [4782983, 4782856, 15]-code), using
- OOA 3-folding [i] based on linear OA(3127, 4782981, F3, 14) (dual of [4782981, 4782854, 15]-code), using
(113, 127, large)-Net in Base 3 — Upper bound on s
There is no (113, 127, large)-net in base 3, because
- 12 times m-reduction [i] would yield (113, 115, large)-net in base 3, but