Best Known (39, 55, s)-Nets in Base 25
(39, 55, 1980)-Net over F25 — Constructive and digital
Digital (39, 55, 1980)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- digital (30, 46, 1953)-net over F25, using
- net defined by OOA [i] based on linear OOA(2546, 1953, F25, 16, 16) (dual of [(1953, 16), 31202, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2546, 15624, F25, 16) (dual of [15624, 15578, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2546, 15624, F25, 16) (dual of [15624, 15578, 17]-code), using
- net defined by OOA [i] based on linear OOA(2546, 1953, F25, 16, 16) (dual of [(1953, 16), 31202, 17]-NRT-code), using
- digital (1, 9, 27)-net over F25, using
(39, 55, 35762)-Net over F25 — Digital
Digital (39, 55, 35762)-net over F25, using
(39, 55, large)-Net in Base 25 — Upper bound on s
There is no (39, 55, large)-net in base 25, because
- 14 times m-reduction [i] would yield (39, 41, large)-net in base 25, but