Best Known (55, 87, s)-Nets in Base 25
(55, 87, 377)-Net over F25 — Constructive and digital
Digital (55, 87, 377)-net over F25, using
- generalized (u, u+v)-construction [i] based on
- digital (9, 19, 125)-net over F25, using
- net defined by OOA [i] based on linear OOA(2519, 125, F25, 10, 10) (dual of [(125, 10), 1231, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2519, 625, F25, 10) (dual of [625, 606, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- OA 5-folding and stacking [i] based on linear OA(2519, 625, F25, 10) (dual of [625, 606, 11]-code), using
- net defined by OOA [i] based on linear OOA(2519, 125, F25, 10, 10) (dual of [(125, 10), 1231, 11]-NRT-code), using
- digital (10, 26, 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 (10, 42, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25 (see above)
- digital (9, 19, 125)-net over F25, using
(55, 87, 4351)-Net over F25 — Digital
Digital (55, 87, 4351)-net over F25, using
(55, 87, large)-Net in Base 25 — Upper bound on s
There is no (55, 87, large)-net in base 25, because
- 30 times m-reduction [i] would yield (55, 57, large)-net in base 25, but