Best Known (40, 40+17, s)-Nets in Base 25
(40, 40+17, 1979)-Net over F25 — Constructive and digital
Digital (40, 57, 1979)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 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 (32, 49, 1953)-net over F25, using
- net defined by OOA [i] based on linear OOA(2549, 1953, F25, 17, 17) (dual of [(1953, 17), 33152, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2549, 15625, F25, 17) (dual of [15625, 15576, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(2549, 15625, F25, 17) (dual of [15625, 15576, 18]-code), using
- net defined by OOA [i] based on linear OOA(2549, 1953, F25, 17, 17) (dual of [(1953, 17), 33152, 18]-NRT-code), using
- digital (0, 8, 26)-net over F25, using
(40, 40+17, 27078)-Net over F25 — Digital
Digital (40, 57, 27078)-net over F25, using
(40, 40+17, large)-Net in Base 25 — Upper bound on s
There is no (40, 57, large)-net in base 25, because
- 15 times m-reduction [i] would yield (40, 42, large)-net in base 25, but