Best Known (68, 68+29, s)-Nets in Base 25
(68, 68+29, 1143)-Net over F25 — Constructive and digital
Digital (68, 97, 1143)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 15, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- digital (53, 82, 1116)-net over F25, using
- net defined by OOA [i] based on linear OOA(2582, 1116, F25, 29, 29) (dual of [(1116, 29), 32282, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2582, 15625, F25, 29) (dual of [15625, 15543, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- OOA 14-folding and stacking with additional row [i] based on linear OA(2582, 15625, F25, 29) (dual of [15625, 15543, 30]-code), using
- net defined by OOA [i] based on linear OOA(2582, 1116, F25, 29, 29) (dual of [(1116, 29), 32282, 30]-NRT-code), using
- digital (1, 15, 27)-net over F25, using
(68, 68+29, 32798)-Net over F25 — Digital
Digital (68, 97, 32798)-net over F25, using
(68, 68+29, large)-Net in Base 25 — Upper bound on s
There is no (68, 97, large)-net in base 25, because
- 27 times m-reduction [i] would yield (68, 70, large)-net in base 25, but