Best Known (55−7, 55, s)-Nets in Base 5
(55−7, 55, 2796226)-Net over F5 — Constructive and digital
Digital (48, 55, 2796226)-net over F5, using
- net defined by OOA [i] based on linear OOA(555, 2796226, F5, 9, 7) (dual of [(2796226, 9), 25165979, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(555, 2796227, F5, 3, 7) (dual of [(2796227, 3), 8388626, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(54, 26, F5, 3, 3) (dual of [(26, 3), 74, 4]-NRT-code), using
- linear OOA(551, 2796201, F5, 3, 7) (dual of [(2796201, 3), 8388552, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(551, large, F5, 7) (dual of [large, large−51, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OOA 3-folding [i] based on linear OA(551, large, F5, 7) (dual of [large, large−51, 8]-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(555, 2796227, F5, 3, 7) (dual of [(2796227, 3), 8388626, 8]-NRT-code), using
(55−7, 55, large)-Net over F5 — Digital
Digital (48, 55, large)-net over F5, using
- 53 times duplication [i] based on digital (45, 52, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(552, large, F5, 7) (dual of [large, large−52, 8]-code), using
- 1 times code embedding in larger space [i] based on linear OA(551, large, F5, 7) (dual of [large, large−51, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 1 times code embedding in larger space [i] based on linear OA(551, large, F5, 7) (dual of [large, large−51, 8]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(552, large, F5, 7) (dual of [large, large−52, 8]-code), using
(55−7, 55, large)-Net in Base 5 — Upper bound on s
There is no (48, 55, large)-net in base 5, because
- 5 times m-reduction [i] would yield (48, 50, large)-net in base 5, but