MinT - Best Known (145−40, 145, s)-Nets in Base 5

Best Known (145−40, 145, s)-Nets in Base 5

(145−40, 145, 408)-Net over F₅ — Constructive and digital

Digital (105, 145, 408)-net over F₅, using

5 times m-reduction [i] based on digital (105, 150, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 75, 204)-net over F₂₅, using
  - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
      - a function field by GarcÃa and Quoos [i]

(145−40, 145, 1547)-Net over F₅ — Digital

Digital (105, 145, 1547)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−40, 145, 242522)-Net in Base 5 — Upper bound on s

There is no (105, 145, 242523)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 224209 046730 416824 602319 952808 059941 845353 504967 521741 581936 391982 880101 161924 089305 783776 424741 752881 > 5¹⁴⁵ [i]