Best Known (73, 73+31, s)-Nets in Base 25
(73, 73+31, 1068)-Net over F25 — Constructive and digital
Digital (73, 104, 1068)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 16, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- digital (57, 88, 1041)-net over F25, using
- net defined by OOA [i] based on linear OOA(2588, 1041, F25, 31, 31) (dual of [(1041, 31), 32183, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(2588, 15616, F25, 31) (dual of [15616, 15528, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2588, 15625, F25, 31) (dual of [15625, 15537, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- discarding factors / shortening the dual code based on linear OA(2588, 15625, F25, 31) (dual of [15625, 15537, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(2588, 15616, F25, 31) (dual of [15616, 15528, 32]-code), using
- net defined by OOA [i] based on linear OOA(2588, 1041, F25, 31, 31) (dual of [(1041, 31), 32183, 32]-NRT-code), using
- digital (1, 16, 27)-net over F25, using
(73, 73+31, 35233)-Net over F25 — Digital
Digital (73, 104, 35233)-net over F25, using
(73, 73+31, large)-Net in Base 25 — Upper bound on s
There is no (73, 104, large)-net in base 25, because
- 29 times m-reduction [i] would yield (73, 75, large)-net in base 25, but