Best Known (35, 50, s)-Nets in Base 25
(35, 50, 2258)-Net over F25 — Constructive and digital
Digital (35, 50, 2258)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 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 (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 (0, 7, 26)-net over F25, using
(35, 50, 24775)-Net over F25 — Digital
Digital (35, 50, 24775)-net over F25, using
(35, 50, large)-Net in Base 25 — Upper bound on s
There is no (35, 50, large)-net in base 25, because
- 13 times m-reduction [i] would yield (35, 37, large)-net in base 25, but