MinT - Best Known (58, 58+49, s)-Nets in Base 5

Best Known (58, 58+49, s)-Nets in Base 5

(58, 58+49, 132)-Net over F₅ — Constructive and digital

Digital (58, 107, 132)-net over F₅, using

1 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+49, 148)-Net over F₅ — Digital

Digital (58, 107, 148)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+49, 2977)-Net in Base 5 — Upper bound on s

There is no (58, 107, 2978)-net in base 5, because

1 times m-reduction [i] would yield (58, 106, 2978)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 123 557821 221737 275956 374853 640040 898254 163776 220677 997006 674769 265547 101825 > 5¹⁰⁶ [i]