Best Known (41, 57, s)-Nets in Base 25
(41, 57, 2005)-Net over F25 — Constructive and digital
Digital (41, 57, 2005)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (3, 11, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-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 (3, 11, 52)-net over F25, using
(41, 57, 54927)-Net over F25 — Digital
Digital (41, 57, 54927)-net over F25, using
(41, 57, large)-Net in Base 25 — Upper bound on s
There is no (41, 57, large)-net in base 25, because
- 14 times m-reduction [i] would yield (41, 43, large)-net in base 25, but