Best Known (136, 150, s)-Nets in Base 5
(136, 150, 2396842)-Net over F5 — Constructive and digital
Digital (136, 150, 2396842)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (11, 18, 100)-net over F5, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 25)-net over F5, using
- s-reduction based on digital (0, 1, s)-net over F5 with arbitrarily large s, using
- digital (1, 3, 25)-net over F5, using
- s-reduction based on digital (1, 3, 31)-net over F5, using
- digital (1, 4, 25)-net over F5, using
- s-reduction based on digital (1, 4, 26)-net over F5, using
- net defined by OOA [i] based on linear OOA(54, 26, F5, 3, 3) (dual of [(26, 3), 74, 4]-NRT-code), using
- s-reduction based on digital (1, 4, 26)-net over F5, using
- digital (3, 10, 25)-net over F5, using
- digital (0, 1, 25)-net over F5, using
- generalized (u, u+v)-construction [i] based on
- digital (118, 132, 2396742)-net over F5, using
- trace code for nets [i] based on digital (52, 66, 1198371)-net over F25, using
- net defined by OOA [i] based on linear OOA(2566, 1198371, F25, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2566, 8388597, F25, 14) (dual of [8388597, 8388531, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2566, large, F25, 14) (dual of [large, large−66, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2566, large, F25, 14) (dual of [large, large−66, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2566, 8388597, F25, 14) (dual of [8388597, 8388531, 15]-code), using
- net defined by OOA [i] based on linear OOA(2566, 1198371, F25, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- trace code for nets [i] based on digital (52, 66, 1198371)-net over F25, using
- digital (11, 18, 100)-net over F5, using
(136, 150, large)-Net over F5 — Digital
Digital (136, 150, large)-net over F5, using
- 54 times duplication [i] based on digital (132, 146, large)-net over F5, using
- t-expansion [i] based on digital (129, 146, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5146, large, F5, 17) (dual of [large, large−146, 18]-code), using
- 15 times code embedding in larger space [i] based on linear OA(5131, large, F5, 17) (dual of [large, large−131, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- 15 times code embedding in larger space [i] based on linear OA(5131, large, F5, 17) (dual of [large, large−131, 18]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5146, large, F5, 17) (dual of [large, large−146, 18]-code), using
- t-expansion [i] based on digital (129, 146, large)-net over F5, using
(136, 150, large)-Net in Base 5 — Upper bound on s
There is no (136, 150, large)-net in base 5, because
- 12 times m-reduction [i] would yield (136, 138, large)-net in base 5, but