MinT - Best Known (55, 55+43, s)-Nets in Base 5

Best Known (55, 55+43, s)-Nets in Base 5

(55, 55+43, 132)-Net over F₅ — Constructive and digital

Digital (55, 98, 132)-net over F₅, using

4 times m-reduction [i] based on digital (55, 102, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 51, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(55, 55+43, 162)-Net over F₅ — Digital

Digital (55, 98, 162)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+43, 3657)-Net in Base 5 — Upper bound on s

There is no (55, 98, 3658)-net in base 5, because

1 times m-reduction [i] would yield (55, 97, 3658)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 63 229464 338617 955334 913292 313081 095252 723916 219409 287350 812224 911145 > 5⁹⁷ [i]