Best Known (74, 74+16, s)-Nets in Base 25
(74, 74+16, 1048653)-Net over F25 — Constructive and digital
Digital (74, 90, 1048653)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (6, 14, 78)-net over F25, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 26)-net over F25, using
- digital (0, 4, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- digital (0, 8, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25 (see above)
- generalized (u, u+v)-construction [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
- digital (6, 14, 78)-net over F25, using
(74, 74+16, large)-Net over F25 — Digital
Digital (74, 90, large)-net over F25, using
- t-expansion [i] based on digital (73, 90, large)-net over F25, using
- 2 times m-reduction [i] based on digital (73, 92, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2592, large, F25, 19) (dual of [large, large−92, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2591, large, F25, 19) (dual of [large, large−91, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times code embedding in larger space [i] based on linear OA(2591, large, F25, 19) (dual of [large, large−91, 20]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2592, large, F25, 19) (dual of [large, large−92, 20]-code), using
- 2 times m-reduction [i] based on digital (73, 92, large)-net over F25, using
(74, 74+16, large)-Net in Base 25 — Upper bound on s
There is no (74, 90, large)-net in base 25, because
- 14 times m-reduction [i] would yield (74, 76, large)-net in base 25, but