Best Known (37, 37+6, s)-Nets in Base 5
(37, 37+6, 2796201)-Net over F5 — Constructive and digital
Digital (37, 43, 2796201)-net over F5, using
- 52 times duplication [i] based on digital (35, 41, 2796201)-net over F5, using
- net defined by OOA [i] based on linear OOA(541, 2796201, F5, 6, 6) (dual of [(2796201, 6), 16777165, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(541, large, F5, 6) (dual of [large, large−41, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(541, large, F5, 6) (dual of [large, large−41, 7]-code), using
- net defined by OOA [i] based on linear OOA(541, 2796201, F5, 6, 6) (dual of [(2796201, 6), 16777165, 7]-NRT-code), using
(37, 37+6, large)-Net over F5 — Digital
Digital (37, 43, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(543, large, F5, 6) (dual of [large, large−43, 7]-code), using
- 2 times code embedding in larger space [i] based on linear OA(541, large, F5, 6) (dual of [large, large−41, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- 2 times code embedding in larger space [i] based on linear OA(541, large, F5, 6) (dual of [large, large−41, 7]-code), using
(37, 37+6, large)-Net in Base 5 — Upper bound on s
There is no (37, 43, large)-net in base 5, because
- 4 times m-reduction [i] would yield (37, 39, large)-net in base 5, but