MinT - Best Known (130−44, 130, s)-Nets in Base 5

Best Known (130−44, 130, s)-Nets in Base 5

(130−44, 130, 296)-Net over F₅ — Constructive and digital

Digital (86, 130, 296)-net over F₅, using

4 times m-reduction [i] based on digital (86, 134, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 67, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(130−44, 130, 553)-Net over F₅ — Digital

Digital (86, 130, 553)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−44, 130, 30538)-Net in Base 5 — Upper bound on s

There is no (86, 130, 30539)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 351273 987487 177135 220452 919723 180110 758611 405937 451445 434777 832095 047906 870151 520942 331305 > 5¹³⁰ [i]