Best Known (63, 72, s)-Nets in Base 5
(63, 72, 2097150)-Net over F5 — Constructive and digital
Digital (63, 72, 2097150)-net over F5, using
- 51 times duplication [i] based on digital (62, 71, 2097150)-net over F5, using
- net defined by OOA [i] based on linear OOA(571, 2097150, F5, 9, 9) (dual of [(2097150, 9), 18874279, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(571, 8388601, F5, 9) (dual of [8388601, 8388530, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(571, large, F5, 9) (dual of [large, large−71, 10]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(571, large, F5, 9) (dual of [large, large−71, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(571, 8388601, F5, 9) (dual of [8388601, 8388530, 10]-code), using
- net defined by OOA [i] based on linear OOA(571, 2097150, F5, 9, 9) (dual of [(2097150, 9), 18874279, 10]-NRT-code), using
(63, 72, large)-Net over F5 — Digital
Digital (63, 72, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(572, large, F5, 9) (dual of [large, large−72, 10]-code), using
- 1 times code embedding in larger space [i] based on linear OA(571, large, F5, 9) (dual of [large, large−71, 10]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 1 times code embedding in larger space [i] based on linear OA(571, large, F5, 9) (dual of [large, large−71, 10]-code), using
(63, 72, large)-Net in Base 5 — Upper bound on s
There is no (63, 72, large)-net in base 5, because
- 7 times m-reduction [i] would yield (63, 65, large)-net in base 5, but