MinT - Best Known (42, 42+35, s)-Nets in Base 5

Best Known (42, 42+35, s)-Nets in Base 5

(42, 42+35, 104)-Net over F₅ — Constructive and digital

Digital (42, 77, 104)-net over F₅, using

1 times m-reduction [i] based on digital (42, 78, 104)-net over F₅, using
- trace code for nets [i] based on digital (3, 39, 52)-net over F₂₅, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by GarcÃa and Quoos [i]

(42, 42+35, 119)-Net over F₅ — Digital

Digital (42, 77, 119)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+35, 2379)-Net in Base 5 — Upper bound on s

There is no (42, 77, 2380)-net in base 5, because

1 times m-reduction [i] would yield (42, 76, 2380)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 132920 746892 016170 450894 192925 346548 444108 270414 533425 > 5⁷⁶ [i]