Best Known (133, 133+17, s)-Nets in Base 5
(133, 133+17, 1048629)-Net over F5 — Constructive and digital
Digital (133, 150, 1048629)-net over F5, using
- 51 times duplication [i] based on digital (132, 149, 1048629)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (10, 18, 54)-net over F5, using
- trace code for nets [i] based on digital (1, 9, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- trace code for nets [i] based on digital (1, 9, 27)-net over F25, using
- digital (114, 131, 1048575)-net over F5, using
- net defined by OOA [i] based on linear OOA(5131, 1048575, F5, 17, 17) (dual of [(1048575, 17), 17825644, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(5131, 8388601, F5, 17) (dual of [8388601, 8388470, 18]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(5131, large, F5, 17) (dual of [large, large−131, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(5131, 8388601, F5, 17) (dual of [8388601, 8388470, 18]-code), using
- net defined by OOA [i] based on linear OOA(5131, 1048575, F5, 17, 17) (dual of [(1048575, 17), 17825644, 18]-NRT-code), using
- digital (10, 18, 54)-net over F5, using
- (u, u+v)-construction [i] based on
(133, 133+17, large)-Net over F5 — Digital
Digital (133, 150, large)-net over F5, using
- 54 times duplication [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
(133, 133+17, large)-Net in Base 5 — Upper bound on s
There is no (133, 150, large)-net in base 5, because
- 15 times m-reduction [i] would yield (133, 135, large)-net in base 5, but