MinT - Best Known (140−40, 140, s)-Nets in Base 5

Best Known (140−40, 140, s)-Nets in Base 5

(140−40, 140, 408)-Net over F₅ — Constructive and digital

Digital (100, 140, 408)-net over F₅, using

trace code for nets [i] based on digital (30, 70, 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]

(140−40, 140, 1262)-Net over F₅ — Digital

Digital (100, 140, 1262)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−40, 140, 162180)-Net in Base 5 — Upper bound on s

There is no (100, 140, 162181)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 71 754840 191653 613847 144590 266961 864838 452217 472785 700069 984308 972098 451069 386704 938119 360789 629105 > 5¹⁴⁰ [i]