Best Known (186−26, 186, s)-Nets in Base 3
(186−26, 186, 4551)-Net over F3 — Constructive and digital
Digital (160, 186, 4551)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (2, 15, 8)-net over F3, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 2 and N(F) ≥ 8, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- digital (145, 171, 4543)-net over F3, using
- net defined by OOA [i] based on linear OOA(3171, 4543, F3, 26, 26) (dual of [(4543, 26), 117947, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3171, 59059, F3, 26) (dual of [59059, 58888, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3161, 59049, F3, 25) (dual of [59049, 58888, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(30, 10, F3, 0) (dual of [10, 10, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- OA 13-folding and stacking [i] based on linear OA(3171, 59059, F3, 26) (dual of [59059, 58888, 27]-code), using
- net defined by OOA [i] based on linear OOA(3171, 4543, F3, 26, 26) (dual of [(4543, 26), 117947, 27]-NRT-code), using
- digital (2, 15, 8)-net over F3, using
(186−26, 186, 29557)-Net over F3 — Digital
Digital (160, 186, 29557)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3186, 29557, F3, 2, 26) (dual of [(29557, 2), 58928, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3186, 59114, F3, 26) (dual of [59114, 58928, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3121, 59049, F3, 19) (dual of [59049, 58928, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(315, 65, F3, 6) (dual of [65, 50, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- OOA 2-folding [i] based on linear OA(3186, 59114, F3, 26) (dual of [59114, 58928, 27]-code), using
(186−26, 186, large)-Net in Base 3 — Upper bound on s
There is no (160, 186, large)-net in base 3, because
- 24 times m-reduction [i] would yield (160, 162, large)-net in base 3, but