Best Known (148, 168, s)-Nets in Base 3
(148, 168, 53152)-Net over F3 — Constructive and digital
Digital (148, 168, 53152)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- digital (137, 157, 53145)-net over F3, using
- net defined by OOA [i] based on linear OOA(3157, 53145, F3, 20, 20) (dual of [(53145, 20), 1062743, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3157, 531450, F3, 20) (dual of [531450, 531293, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3157, 531453, F3, 20) (dual of [531453, 531296, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(3157, 531441, F3, 20) (dual of [531441, 531284, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3145, 531441, F3, 19) (dual of [531441, 531296, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(30, 12, F3, 0) (dual of [12, 12, 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(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3157, 531453, F3, 20) (dual of [531453, 531296, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3157, 531450, F3, 20) (dual of [531450, 531293, 21]-code), using
- net defined by OOA [i] based on linear OOA(3157, 53145, F3, 20, 20) (dual of [(53145, 20), 1062743, 21]-NRT-code), using
- digital (1, 11, 7)-net over F3, using
(148, 168, 177166)-Net over F3 — Digital
Digital (148, 168, 177166)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3168, 177166, F3, 3, 20) (dual of [(177166, 3), 531330, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3168, 531498, F3, 20) (dual of [531498, 531330, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3168, 531500, F3, 20) (dual of [531500, 531332, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(3157, 531441, F3, 20) (dual of [531441, 531284, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3109, 531441, F3, 14) (dual of [531441, 531332, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(311, 59, F3, 5) (dual of [59, 48, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(3168, 531500, F3, 20) (dual of [531500, 531332, 21]-code), using
- OOA 3-folding [i] based on linear OA(3168, 531498, F3, 20) (dual of [531498, 531330, 21]-code), using
(148, 168, large)-Net in Base 3 — Upper bound on s
There is no (148, 168, large)-net in base 3, because
- 18 times m-reduction [i] would yield (148, 150, large)-net in base 3, but