Best Known (61, 61+16, s)-Nets in Base 25
(61, 61+16, 1048575)-Net over F25 — Constructive and digital
Digital (61, 77, 1048575)-net over F25, using
- 251 times duplication [i] based on digital (60, 76, 1048575)-net over F25, using
- net defined by OOA [i] based on linear OOA(2576, 1048575, F25, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2576, 8388600, F25, 16) (dual of [8388600, 8388524, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2576, large, F25, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2576, large, F25, 16) (dual of [large, large−76, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2576, 8388600, F25, 16) (dual of [8388600, 8388524, 17]-code), using
- net defined by OOA [i] based on linear OOA(2576, 1048575, F25, 16, 16) (dual of [(1048575, 16), 16777124, 17]-NRT-code), using
(61, 61+16, large)-Net over F25 — Digital
Digital (61, 77, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2577, large, F25, 16) (dual of [large, large−77, 17]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2576, large, F25, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 1 times code embedding in larger space [i] based on linear OA(2576, large, F25, 16) (dual of [large, large−76, 17]-code), using
(61, 61+16, large)-Net in Base 25 — Upper bound on s
There is no (61, 77, large)-net in base 25, because
- 14 times m-reduction [i] would yield (61, 63, large)-net in base 25, but