Best Known (125, 125+10, s)-Nets in Base 3
(125, 125+10, 3355444)-Net over F3 — Constructive and digital
Digital (125, 135, 3355444)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 4)-net over F3, using
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 0 and N(F) ≥ 4, using
- the rational function field F3(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- digital (120, 130, 3355440)-net over F3, using
- trace code for nets [i] based on digital (55, 65, 1677720)-net over F9, using
- net defined by OOA [i] based on linear OOA(965, 1677720, F9, 10, 10) (dual of [(1677720, 10), 16777135, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(965, 8388600, F9, 10) (dual of [8388600, 8388535, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(965, large, F9, 10) (dual of [large, large−65, 11]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(965, large, F9, 10) (dual of [large, large−65, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(965, 8388600, F9, 10) (dual of [8388600, 8388535, 11]-code), using
- net defined by OOA [i] based on linear OOA(965, 1677720, F9, 10, 10) (dual of [(1677720, 10), 16777135, 11]-NRT-code), using
- trace code for nets [i] based on digital (55, 65, 1677720)-net over F9, using
- digital (0, 5, 4)-net over F3, using
(125, 125+10, large)-Net over F3 — Digital
Digital (125, 135, large)-net over F3, using
- 39 times duplication [i] based on digital (116, 126, large)-net over F3, using
- t-expansion [i] based on digital (115, 126, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3126, large, F3, 11) (dual of [large, large−126, 12]-code), using
- 20 times code embedding in larger space [i] based on linear OA(3106, large, F3, 11) (dual of [large, large−106, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- 20 times code embedding in larger space [i] based on linear OA(3106, large, F3, 11) (dual of [large, large−106, 12]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3126, large, F3, 11) (dual of [large, large−126, 12]-code), using
- t-expansion [i] based on digital (115, 126, large)-net over F3, using
(125, 125+10, large)-Net in Base 3 — Upper bound on s
There is no (125, 135, large)-net in base 3, because
- 8 times m-reduction [i] would yield (125, 127, large)-net in base 3, but