MinT - Best Known (137−59, 137, s)-Nets in Base 5

Best Known (137−59, 137, s)-Nets in Base 5

(137−59, 137, 208)-Net over F₅ — Constructive and digital

Digital (78, 137, 208)-net over F₅, using

1 times m-reduction [i] based on digital (78, 138, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 69, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]

(137−59, 137, 226)-Net over F₅ — Digital

Digital (78, 137, 226)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−59, 137, 5512)-Net in Base 5 — Upper bound on s

There is no (78, 137, 5513)-net in base 5, because

1 times m-reduction [i] would yield (78, 136, 5513)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 115302 554257 941580 542287 496755 914025 377748 581950 532835 084355 382920 526077 048523 474423 472826 692725 > 5¹³⁶ [i]