Best Known (120, 120+21, s)-Nets in Base 3
(120, 120+21, 5905)-Net over F3 — Constructive and digital
Digital (120, 141, 5905)-net over F3, using
- net defined by OOA [i] based on linear OOA(3141, 5905, F3, 21, 21) (dual of [(5905, 21), 123864, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3141, 59051, F3, 21) (dual of [59051, 58910, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3141, 59059, F3, 21) (dual of [59059, 58918, 22]-code), using
- 1 times truncation [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 truncation [i] based on linear OA(3142, 59060, F3, 22) (dual of [59060, 58918, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3141, 59059, F3, 21) (dual of [59059, 58918, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3141, 59051, F3, 21) (dual of [59051, 58910, 22]-code), using
(120, 120+21, 19686)-Net over F3 — Digital
Digital (120, 141, 19686)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3141, 19686, F3, 3, 21) (dual of [(19686, 3), 58917, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3141, 59058, F3, 21) (dual of [59058, 58917, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3141, 59059, F3, 21) (dual of [59059, 58918, 22]-code), using
- 1 times truncation [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 truncation [i] based on linear OA(3142, 59060, F3, 22) (dual of [59060, 58918, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3141, 59059, F3, 21) (dual of [59059, 58918, 22]-code), using
- OOA 3-folding [i] based on linear OA(3141, 59058, F3, 21) (dual of [59058, 58917, 22]-code), using
(120, 120+21, large)-Net in Base 3 — Upper bound on s
There is no (120, 141, large)-net in base 3, because
- 19 times m-reduction [i] would yield (120, 122, large)-net in base 3, but