Best Known (41−5, 41, s)-Nets in Base 5
(41−5, 41, 4194301)-Net over F5 — Constructive and digital
Digital (36, 41, 4194301)-net over F5, using
- 51 times duplication [i] based on digital (35, 40, 4194301)-net over F5, using
- net defined by OOA [i] based on linear OOA(540, 4194301, F5, 5, 5) (dual of [(4194301, 5), 20971465, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(540, large, F5, 5) (dual of [large, large−40, 6]-code), using
- the primitive narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(540, large, F5, 5) (dual of [large, large−40, 6]-code), using
- net defined by OOA [i] based on linear OOA(540, 4194301, F5, 5, 5) (dual of [(4194301, 5), 20971465, 6]-NRT-code), using
(41−5, 41, large)-Net over F5 — Digital
Digital (36, 41, large)-net over F5, using
- 51 times duplication [i] based on digital (35, 40, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(540, large, F5, 5) (dual of [large, large−40, 6]-code), using
- the primitive narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(540, large, F5, 5) (dual of [large, large−40, 6]-code), using
(41−5, 41, large)-Net in Base 5 — Upper bound on s
There is no (36, 41, large)-net in base 5, because
- 3 times m-reduction [i] would yield (36, 38, large)-net in base 5, but