Best Known (89−25, 89, s)-Nets in Base 25
(89−25, 89, 1368)-Net over F25 — Constructive and digital
Digital (64, 89, 1368)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 16, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- digital (48, 73, 1302)-net over F25, using
- net defined by OOA [i] based on linear OOA(2573, 1302, F25, 25, 25) (dual of [(1302, 25), 32477, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2573, 15625, F25, 25) (dual of [15625, 15552, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2573, 15626, F25, 25) (dual of [15626, 15553, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2573, 15626, F25, 25) (dual of [15626, 15553, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2573, 15625, F25, 25) (dual of [15625, 15552, 26]-code), using
- net defined by OOA [i] based on linear OOA(2573, 1302, F25, 25, 25) (dual of [(1302, 25), 32477, 26]-NRT-code), using
- digital (4, 16, 66)-net over F25, using
(89−25, 89, 62411)-Net over F25 — Digital
Digital (64, 89, 62411)-net over F25, using
(89−25, 89, large)-Net in Base 25 — Upper bound on s
There is no (64, 89, large)-net in base 25, because
- 23 times m-reduction [i] would yield (64, 66, large)-net in base 25, but