Best Known (89−24, 89, s)-Nets in Base 25
(89−24, 89, 1369)-Net over F25 — Constructive and digital
Digital (65, 89, 1369)-net over F25, using
- 251 times duplication [i] based on digital (64, 88, 1369)-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, 72, 1303)-net over F25, using
- net defined by OOA [i] based on linear OOA(2572, 1303, F25, 24, 24) (dual of [(1303, 24), 31200, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2572, 15636, F25, 24) (dual of [15636, 15564, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(2570, 15625, F25, 24) (dual of [15625, 15555, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2561, 15625, F25, 21) (dual of [15625, 15564, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(252, 11, F25, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- OA 12-folding and stacking [i] based on linear OA(2572, 15636, F25, 24) (dual of [15636, 15564, 25]-code), using
- net defined by OOA [i] based on linear OOA(2572, 1303, F25, 24, 24) (dual of [(1303, 24), 31200, 25]-NRT-code), using
- digital (4, 16, 66)-net over F25, using
- (u, u+v)-construction [i] based on
(89−24, 89, 100859)-Net over F25 — Digital
Digital (65, 89, 100859)-net over F25, using
(89−24, 89, large)-Net in Base 25 — Upper bound on s
There is no (65, 89, large)-net in base 25, because
- 22 times m-reduction [i] would yield (65, 67, large)-net in base 25, but