MinT - Best Known (60, 60+43, s)-Nets in Base 5

Best Known (60, 60+43, s)-Nets in Base 5

(60, 60+43, 132)-Net over F₅ — Constructive and digital

Digital (60, 103, 132)-net over F₅, using

9 times m-reduction [i] based on digital (60, 112, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 56, 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]

(60, 60+43, 200)-Net over F₅ — Digital

Digital (60, 103, 200)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+43, 5372)-Net in Base 5 — Upper bound on s

There is no (60, 103, 5373)-net in base 5, because

1 times m-reduction [i] would yield (60, 102, 5373)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 197374 961381 335669 823320 753971 474402 748526 339546 240706 089626 140835 294693 > 5¹⁰² [i]