Best Known (68, 68+25, s)-Nets in Base 25
(68, 68+25, 1405)-Net over F25 — Constructive and digital
Digital (68, 93, 1405)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (9, 21, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- digital (47, 72, 1301)-net over F25, using
- net defined by OOA [i] based on linear OOA(2572, 1301, F25, 25, 25) (dual of [(1301, 25), 32453, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2572, 15613, F25, 25) (dual of [15613, 15541, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2572, 15624, F25, 25) (dual of [15624, 15552, 26]-code), using
- 1 times truncation [i] based on linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 1 times truncation [i] based on linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2572, 15624, F25, 25) (dual of [15624, 15552, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2572, 15613, F25, 25) (dual of [15613, 15541, 26]-code), using
- net defined by OOA [i] based on linear OOA(2572, 1301, F25, 25, 25) (dual of [(1301, 25), 32453, 26]-NRT-code), using
- digital (9, 21, 104)-net over F25, using
(68, 68+25, 106713)-Net over F25 — Digital
Digital (68, 93, 106713)-net over F25, using
(68, 68+25, large)-Net in Base 25 — Upper bound on s
There is no (68, 93, large)-net in base 25, because
- 23 times m-reduction [i] would yield (68, 70, large)-net in base 25, but