Best Known (144−14, 144, s)-Nets in Base 5
(144−14, 144, 2396767)-Net over F5 — Constructive and digital
Digital (130, 144, 2396767)-net over F5, using
- 52 times duplication [i] based on digital (128, 142, 2396767)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (3, 10, 25)-net over F5, using
- 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
- (u, u+v)-construction [i] based on
(144−14, 144, large)-Net over F5 — Digital
Digital (130, 144, large)-net over F5, using
- t-expansion [i] based on digital (129, 144, large)-net over F5, using
- 2 times m-reduction [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
- 2 times m-reduction [i] based on digital (129, 146, large)-net over F5, using
(144−14, 144, large)-Net in Base 5 — Upper bound on s
There is no (130, 144, large)-net in base 5, because
- 12 times m-reduction [i] would yield (130, 132, large)-net in base 5, but