MinT - Best Known (108, 108+42, s)-Nets in Base 5

Best Known (108, 108+42, s)-Nets in Base 5

(108, 108+42, 408)-Net over F₅ — Constructive and digital

Digital (108, 150, 408)-net over F₅, using

t-expansion [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]

(108, 108+42, 1476)-Net over F₅ — Digital

Digital (108, 150, 1476)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+42, 213326)-Net in Base 5 — Upper bound on s

There is no (108, 150, 213327)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 700 696875 999477 041208 653893 128514 722835 619215 964686 000652 243276 707426 249852 204085 529545 965509 783980 136685 > 5¹⁵⁰ [i]