MinT - Best Known (58, 58+42, s)-Nets in Base 5

Best Known (58, 58+42, s)-Nets in Base 5

(58, 58+42, 132)-Net over F₅ — Constructive and digital

Digital (58, 100, 132)-net over F₅, using

8 times m-reduction [i] based on digital (58, 108, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 54, 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]

(58, 58+42, 192)-Net over F₅ — Digital

Digital (58, 100, 192)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+42, 4607)-Net in Base 5 — Upper bound on s

There is no (58, 100, 4608)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7920 910107 520983 707534 508914 184820 286686 721842 264548 419443 523510 831105 > 5¹⁰⁰ [i]