MinT - Best Known (70, 70+51, s)-Nets in Base 5

Best Known (70, 70+51, s)-Nets in Base 5

(70, 70+51, 208)-Net over F₅ — Constructive and digital

Digital (70, 121, 208)-net over F₅, using

1 times m-reduction [i] based on digital (70, 122, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 61, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]

(70, 70+51, 222)-Net over F₅ — Digital

Digital (70, 121, 222)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+51, 5744)-Net in Base 5 — Upper bound on s

There is no (70, 121, 5745)-net in base 5, because

1 times m-reduction [i] would yield (70, 120, 5745)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 754225 991875 026947 095942 694001 168614 771314 344483 289757 441735 200701 568811 934959 830501 > 5¹²⁰ [i]