Best Known (132−14, 132, s)-Nets in Base 3
(132−14, 132, 683286)-Net over F3 — Constructive and digital
Digital (118, 132, 683286)-net over F3, using
- net defined by OOA [i] based on linear OOA(3132, 683286, F3, 14, 14) (dual of [(683286, 14), 9565872, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3132, 4783002, F3, 14) (dual of [4783002, 4782870, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3131, 4783001, F3, 14) (dual of [4783001, 4782870, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [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(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(34, 32, F3, 2) (dual of [32, 28, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3131, 4783001, F3, 14) (dual of [4783001, 4782870, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3132, 4783002, F3, 14) (dual of [4783002, 4782870, 15]-code), using
(132−14, 132, 1594334)-Net over F3 — Digital
Digital (118, 132, 1594334)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3132, 1594334, F3, 3, 14) (dual of [(1594334, 3), 4782870, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3132, 4783002, F3, 14) (dual of [4783002, 4782870, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3131, 4783001, F3, 14) (dual of [4783001, 4782870, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [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(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(34, 32, F3, 2) (dual of [32, 28, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3131, 4783001, F3, 14) (dual of [4783001, 4782870, 15]-code), using
- OOA 3-folding [i] based on linear OA(3132, 4783002, F3, 14) (dual of [4783002, 4782870, 15]-code), using
(132−14, 132, large)-Net in Base 3 — Upper bound on s
There is no (118, 132, large)-net in base 3, because
- 12 times m-reduction [i] would yield (118, 120, large)-net in base 3, but