MinT - Best Known (40, 71, s)-Nets in Base 4

Best Known (40, 71, s)-Nets in Base 4

(40, 71, 90)-Net over F₄ — Constructive and digital

Digital (40, 71, 90)-net over F₄, using

1 times m-reduction [i] based on digital (40, 72, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 36, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(40, 71, 95)-Net over F₄ — Digital

Digital (40, 71, 95)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 71, 1369)-Net in Base 4 — Upper bound on s

There is no (40, 71, 1370)-net in base 4, because

1 times m-reduction [i] would yield (40, 70, 1370)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 405237 291098 215586 327091 069154 208089 660872 > 4⁷⁰ [i]