Best Known (39, 54, s)-Nets in Base 25
(39, 54, 2298)-Net over F25 — Constructive and digital
Digital (39, 54, 2298)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 11, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- digital (28, 43, 2232)-net over F25, using
- net defined by OOA [i] based on linear OOA(2543, 2232, F25, 15, 15) (dual of [(2232, 15), 33437, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2543, 15625, F25, 15) (dual of [15625, 15582, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(2543, 15625, F25, 15) (dual of [15625, 15582, 16]-code), using
- net defined by OOA [i] based on linear OOA(2543, 2232, F25, 15, 15) (dual of [(2232, 15), 33437, 16]-NRT-code), using
- digital (4, 11, 66)-net over F25, using
(39, 54, 62137)-Net over F25 — Digital
Digital (39, 54, 62137)-net over F25, using
(39, 54, large)-Net in Base 25 — Upper bound on s
There is no (39, 54, large)-net in base 25, because
- 13 times m-reduction [i] would yield (39, 41, large)-net in base 25, but