Best Known (26, 44, s)-Nets in Base 25
(26, 44, 208)-Net over F25 — Constructive and digital
Digital (26, 44, 208)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (8, 17, 156)-net over F25, using
- net defined by OOA [i] based on linear OOA(2517, 156, F25, 9, 9) (dual of [(156, 9), 1387, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2517, 625, F25, 9) (dual of [625, 608, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(2517, 625, F25, 9) (dual of [625, 608, 10]-code), using
- net defined by OOA [i] based on linear OOA(2517, 156, F25, 9, 9) (dual of [(156, 9), 1387, 10]-NRT-code), using
- digital (9, 27, 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 (8, 17, 156)-net over F25, using
(26, 44, 1250)-Net over F25 — Digital
Digital (26, 44, 1250)-net over F25, using
(26, 44, 1180081)-Net in Base 25 — Upper bound on s
There is no (26, 44, 1180082)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 32 311885 982582 290353 499762 620927 843396 221663 876289 450220 575025 > 2544 [i]