Best Known (51, 51+16, s)-Nets in Base 25
(51, 51+16, 48831)-Net over F25 — Constructive and digital
Digital (51, 67, 48831)-net over F25, using
- 252 times duplication [i] based on digital (49, 65, 48831)-net over F25, using
- net defined by OOA [i] based on linear OOA(2565, 48831, F25, 16, 16) (dual of [(48831, 16), 781231, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2565, 390648, F25, 16) (dual of [390648, 390583, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2565, 390649, F25, 16) (dual of [390649, 390584, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(2561, 390625, F25, 16) (dual of [390625, 390564, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2541, 390625, F25, 11) (dual of [390625, 390584, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(254, 24, F25, 4) (dual of [24, 20, 5]-code or 24-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(2565, 390649, F25, 16) (dual of [390649, 390584, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2565, 390648, F25, 16) (dual of [390648, 390583, 17]-code), using
- net defined by OOA [i] based on linear OOA(2565, 48831, F25, 16, 16) (dual of [(48831, 16), 781231, 17]-NRT-code), using
(51, 51+16, 469564)-Net over F25 — Digital
Digital (51, 67, 469564)-net over F25, using
(51, 51+16, large)-Net in Base 25 — Upper bound on s
There is no (51, 67, large)-net in base 25, because
- 14 times m-reduction [i] would yield (51, 53, large)-net in base 25, but