Best Known (70, 70+26, s)-Nets in Base 25
(70, 70+26, 1327)-Net over F25 — Constructive and digital
Digital (70, 96, 1327)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (10, 23, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- digital (47, 73, 1201)-net over F25, using
- net defined by OOA [i] based on linear OOA(2573, 1201, F25, 26, 26) (dual of [(1201, 26), 31153, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(2573, 15613, F25, 26) (dual of [15613, 15540, 27]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(2573, 15613, F25, 26) (dual of [15613, 15540, 27]-code), using
- net defined by OOA [i] based on linear OOA(2573, 1201, F25, 26, 26) (dual of [(1201, 26), 31153, 27]-NRT-code), using
- digital (10, 23, 126)-net over F25, using
(70, 70+26, 98983)-Net over F25 — Digital
Digital (70, 96, 98983)-net over F25, using
(70, 70+26, large)-Net in Base 25 — Upper bound on s
There is no (70, 96, large)-net in base 25, because
- 24 times m-reduction [i] would yield (70, 72, large)-net in base 25, but