MinT - Best Known (52, 52+41, s)-Nets in Base 5

Best Known (52, 52+41, s)-Nets in Base 5

(52, 52+41, 132)-Net over F₅ — Constructive and digital

Digital (52, 93, 132)-net over F₅, using

3 times m-reduction [i] based on digital (52, 96, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 48, 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]

(52, 52+41, 153)-Net over F₅ — Digital

Digital (52, 93, 153)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+41, 3393)-Net in Base 5 — Upper bound on s

There is no (52, 93, 3394)-net in base 5, because

1 times m-reduction [i] would yield (52, 92, 3394)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 20243 447354 706188 532983 929555 095086 807979 839474 443347 513709 717825 > 5⁹² [i]