MinT - Best Known (141−41, 141, s)-Nets in Base 5

Best Known (141−41, 141, s)-Nets in Base 5

(141−41, 141, 400)-Net over F₅ — Constructive and digital

Digital (100, 141, 400)-net over F₅, using

9 times m-reduction [i] based on digital (100, 150, 400)-net over F₅, using
- trace code for nets [i] based on digital (25, 75, 200)-net over F₂₅, using
  - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
      - a function field by GarcÃa and Quoos [i]

(141−41, 141, 1167)-Net over F₅ — Digital

Digital (100, 141, 1167)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−41, 141, 162180)-Net in Base 5 — Upper bound on s

There is no (100, 141, 162181)-net in base 5, because

1 times m-reduction [i] would yield (100, 140, 162181)-net in base 5, but
- 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]