Best Known (119, 119+15, s)-Nets in Base 5
(119, 119+15, 1198423)-Net over F5 — Constructive and digital
Digital (119, 134, 1198423)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (7, 14, 52)-net over F5, using
- trace code for nets [i] based on digital (0, 7, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- trace code for nets [i] based on digital (0, 7, 26)-net over F25, using
- digital (105, 120, 1198371)-net over F5, using
- net defined by OOA [i] based on linear OOA(5120, 1198371, F5, 15, 15) (dual of [(1198371, 15), 17975445, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(5120, 8388598, F5, 15) (dual of [8388598, 8388478, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(5120, large, F5, 15) (dual of [large, large−120, 16]-code), using
- the primitive narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(5120, large, F5, 15) (dual of [large, large−120, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(5120, 8388598, F5, 15) (dual of [8388598, 8388478, 16]-code), using
- net defined by OOA [i] based on linear OOA(5120, 1198371, F5, 15, 15) (dual of [(1198371, 15), 17975445, 16]-NRT-code), using
- digital (7, 14, 52)-net over F5, using
(119, 119+15, large)-Net over F5 — Digital
Digital (119, 134, large)-net over F5, using
- 57 times duplication [i] based on digital (112, 127, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5127, large, F5, 15) (dual of [large, large−127, 16]-code), using
- 7 times code embedding in larger space [i] based on linear OA(5120, large, F5, 15) (dual of [large, large−120, 16]-code), using
- the primitive narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- 7 times code embedding in larger space [i] based on linear OA(5120, large, F5, 15) (dual of [large, large−120, 16]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5127, large, F5, 15) (dual of [large, large−127, 16]-code), using
(119, 119+15, large)-Net in Base 5 — Upper bound on s
There is no (119, 134, large)-net in base 5, because
- 13 times m-reduction [i] would yield (119, 121, large)-net in base 5, but