MinT - Best Known (139−63, 139, s)-Nets in Base 5

Best Known (139−63, 139, s)-Nets in Base 5

(139−63, 139, 132)-Net over F₅ — Constructive and digital

Digital (76, 139, 132)-net over F₅, using

5 times m-reduction [i] based on digital (76, 144, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 72, 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]

(139−63, 139, 191)-Net over F₅ — Digital

Digital (76, 139, 191)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−63, 139, 3990)-Net in Base 5 — Upper bound on s

There is no (76, 139, 3991)-net in base 5, because

1 times m-reduction [i] would yield (76, 138, 3991)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 875698 879061 956652 941896 254164 314016 445792 943362 438820 142893 616473 528923 002188 662489 218862 200165 > 5¹³⁸ [i]