Best Known (169, 169+28, s)-Nets in Base 3
(169, 169+28, 4225)-Net over F3 — Constructive and digital
Digital (169, 197, 4225)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (2, 16, 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 (153, 181, 4217)-net over F3, using
- net defined by OOA [i] based on linear OOA(3181, 4217, F3, 28, 28) (dual of [(4217, 28), 117895, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3181, 59038, F3, 28) (dual of [59038, 58857, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3181, 59038, F3, 28) (dual of [59038, 58857, 29]-code), using
- net defined by OOA [i] based on linear OOA(3181, 4217, F3, 28, 28) (dual of [(4217, 28), 117895, 29]-NRT-code), using
- digital (2, 16, 8)-net over F3, using
(169, 169+28, 26776)-Net over F3 — Digital
Digital (169, 197, 26776)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3197, 26776, F3, 2, 28) (dual of [(26776, 2), 53355, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3197, 29557, F3, 2, 28) (dual of [(29557, 2), 58917, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3197, 59114, F3, 28) (dual of [59114, 58917, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3197, 59115, F3, 28) (dual of [59115, 58918, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(19) [i] based on
- linear OA(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(316, 66, F3, 7) (dual of [66, 50, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
- construction X applied to Ce(27) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3197, 59115, F3, 28) (dual of [59115, 58918, 29]-code), using
- OOA 2-folding [i] based on linear OA(3197, 59114, F3, 28) (dual of [59114, 58917, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(3197, 29557, F3, 2, 28) (dual of [(29557, 2), 58917, 29]-NRT-code), using
(169, 169+28, large)-Net in Base 3 — Upper bound on s
There is no (169, 197, large)-net in base 3, because
- 26 times m-reduction [i] would yield (169, 171, large)-net in base 3, but