Best Known (158, 176, s)-Nets in Base 3
(158, 176, 531446)-Net over F3 — Constructive and digital
Digital (158, 176, 531446)-net over F3, using
- 31 times duplication [i] based on digital (157, 175, 531446)-net over F3, using
- net defined by OOA [i] based on linear OOA(3175, 531446, F3, 18, 18) (dual of [(531446, 18), 9565853, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3175, 4783014, F3, 18) (dual of [4783014, 4782839, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3175, 4783017, F3, 18) (dual of [4783017, 4782842, 19]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(3169, 4782969, F3, 19) (dual of [4782969, 4782800, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(3175, 4783017, F3, 18) (dual of [4783017, 4782842, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(3175, 4783014, F3, 18) (dual of [4783014, 4782839, 19]-code), using
- net defined by OOA [i] based on linear OOA(3175, 531446, F3, 18, 18) (dual of [(531446, 18), 9565853, 19]-NRT-code), using
(158, 176, 1594339)-Net over F3 — Digital
Digital (158, 176, 1594339)-net over F3, using
- 31 times duplication [i] based on digital (157, 175, 1594339)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3175, 1594339, F3, 3, 18) (dual of [(1594339, 3), 4782842, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3175, 4783017, F3, 18) (dual of [4783017, 4782842, 19]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(3169, 4782969, F3, 19) (dual of [4782969, 4782800, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- OOA 3-folding [i] based on linear OA(3175, 4783017, F3, 18) (dual of [4783017, 4782842, 19]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3175, 1594339, F3, 3, 18) (dual of [(1594339, 3), 4782842, 19]-NRT-code), using
(158, 176, large)-Net in Base 3 — Upper bound on s
There is no (158, 176, large)-net in base 3, because
- 16 times m-reduction [i] would yield (158, 160, large)-net in base 3, but