Best Known (99−29, 99, s)-Nets in Base 25
(99−29, 99, 1168)-Net over F25 — Constructive and digital
Digital (70, 99, 1168)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (3, 17, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- digital (53, 82, 1116)-net over F25, using
- net defined by OOA [i] based on linear OOA(2582, 1116, F25, 29, 29) (dual of [(1116, 29), 32282, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2582, 15625, F25, 29) (dual of [15625, 15543, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- OOA 14-folding and stacking with additional row [i] based on linear OA(2582, 15625, F25, 29) (dual of [15625, 15543, 30]-code), using
- net defined by OOA [i] based on linear OOA(2582, 1116, F25, 29, 29) (dual of [(1116, 29), 32282, 30]-NRT-code), using
- digital (3, 17, 52)-net over F25, using
(99−29, 99, 41272)-Net over F25 — Digital
Digital (70, 99, 41272)-net over F25, using
(99−29, 99, large)-Net in Base 25 — Upper bound on s
There is no (70, 99, large)-net in base 25, because
- 27 times m-reduction [i] would yield (70, 72, large)-net in base 25, but