Best Known (134−14, 134, s)-Nets in Base 3
(134−14, 134, 683288)-Net over F3 — Constructive and digital
Digital (120, 134, 683288)-net over F3, using
- 31 times duplication [i] based on digital (119, 133, 683288)-net over F3, using
- net defined by OOA [i] based on linear OOA(3133, 683288, F3, 14, 14) (dual of [(683288, 14), 9565899, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3133, 4783016, F3, 14) (dual of [4783016, 4782883, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3133, 4783017, F3, 14) (dual of [4783017, 4782884, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [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(385, 4782969, F3, 10) (dual of [4782969, 4782884, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(3133, 4783017, F3, 14) (dual of [4783017, 4782884, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3133, 4783016, F3, 14) (dual of [4783016, 4782883, 15]-code), using
- net defined by OOA [i] based on linear OOA(3133, 683288, F3, 14, 14) (dual of [(683288, 14), 9565899, 15]-NRT-code), using
(134−14, 134, 1594339)-Net over F3 — Digital
Digital (120, 134, 1594339)-net over F3, using
- 31 times duplication [i] based on digital (119, 133, 1594339)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3133, 1594339, F3, 3, 14) (dual of [(1594339, 3), 4782884, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3133, 4783017, F3, 14) (dual of [4783017, 4782884, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [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(385, 4782969, F3, 10) (dual of [4782969, 4782884, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- OOA 3-folding [i] based on linear OA(3133, 4783017, F3, 14) (dual of [4783017, 4782884, 15]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3133, 1594339, F3, 3, 14) (dual of [(1594339, 3), 4782884, 15]-NRT-code), using
(134−14, 134, large)-Net in Base 3 — Upper bound on s
There is no (120, 134, large)-net in base 3, because
- 12 times m-reduction [i] would yield (120, 122, large)-net in base 3, but