MinT - Best Known (58, 58+45, s)-Nets in Base 5

Best Known (58, 58+45, s)-Nets in Base 5

(58, 58+45, 132)-Net over F₅ — Constructive and digital

Digital (58, 103, 132)-net over F₅, using

5 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+45, 171)-Net over F₅ — Digital

Digital (58, 103, 171)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+45, 3923)-Net in Base 5 — Upper bound on s

There is no (58, 103, 3924)-net in base 5, because

1 times m-reduction [i] would yield (58, 102, 3924)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 197430 112150 214367 283343 388733 248844 306538 414238 936784 720990 905496 062913 > 5¹⁰² [i]