MinT - Best Known (71, 71+59, s)-Nets in Base 5

Best Known (71, 71+59, s)-Nets in Base 5

(71, 71+59, 132)-Net over F₅ — Constructive and digital

Digital (71, 130, 132)-net over F₅, using

4 times m-reduction [i] based on digital (71, 134, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 67, 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]

(71, 71+59, 180)-Net over F₅ — Digital

Digital (71, 130, 180)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+59, 3730)-Net in Base 5 — Upper bound on s

There is no (71, 130, 3731)-net in base 5, because

1 times m-reduction [i] would yield (71, 129, 3731)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 470678 524492 400726 760063 401049 505804 384601 831762 447292 773195 988246 454003 853784 638898 467805 > 5¹²⁹ [i]