Best Known (143−22, 143, s)-Nets in Base 3
(143−22, 143, 5369)-Net over F3 — Constructive and digital
Digital (121, 143, 5369)-net over F3, using
- 31 times duplication [i] based on digital (120, 142, 5369)-net over F3, using
- net defined by OOA [i] based on linear OOA(3142, 5369, F3, 22, 22) (dual of [(5369, 22), 117976, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3142, 59059, F3, 22) (dual of [59059, 58917, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3142, 59060, F3, 22) (dual of [59060, 58918, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(3141, 59049, F3, 22) (dual of [59049, 58908, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3131, 59049, F3, 20) (dual of [59049, 58918, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3142, 59060, F3, 22) (dual of [59060, 58918, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3142, 59059, F3, 22) (dual of [59059, 58917, 23]-code), using
- net defined by OOA [i] based on linear OOA(3142, 5369, F3, 22, 22) (dual of [(5369, 22), 117976, 23]-NRT-code), using
(143−22, 143, 19394)-Net over F3 — Digital
Digital (121, 143, 19394)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3143, 19394, F3, 3, 22) (dual of [(19394, 3), 58039, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3143, 19687, F3, 3, 22) (dual of [(19687, 3), 58918, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3143, 59061, F3, 22) (dual of [59061, 58918, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3142, 59060, F3, 22) (dual of [59060, 58918, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(3141, 59049, F3, 22) (dual of [59049, 58908, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3131, 59049, F3, 20) (dual of [59049, 58918, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3142, 59060, F3, 22) (dual of [59060, 58918, 23]-code), using
- OOA 3-folding [i] based on linear OA(3143, 59061, F3, 22) (dual of [59061, 58918, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(3143, 19687, F3, 3, 22) (dual of [(19687, 3), 58918, 23]-NRT-code), using
(143−22, 143, 3913445)-Net in Base 3 — Upper bound on s
There is no (121, 143, 3913446)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 169 176428 735629 315536 478935 375103 776297 142352 417772 270057 448024 791953 > 3143 [i]