Best Known (52−15, 52, s)-Nets in Base 25
(52−15, 52, 2260)-Net over F25 — Constructive and digital
Digital (37, 52, 2260)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (2, 9, 28)-net over F25, using
- net from sequence [i] based on digital (2, 27)-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 (2, 9, 28)-net over F25, using
(52−15, 52, 39235)-Net over F25 — Digital
Digital (37, 52, 39235)-net over F25, using
(52−15, 52, large)-Net in Base 25 — Upper bound on s
There is no (37, 52, large)-net in base 25, because
- 13 times m-reduction [i] would yield (37, 39, large)-net in base 25, but