MinT - Best Known (78, 78+39, s)-Nets in Base 5

Best Known (78, 78+39, s)-Nets in Base 5

(78, 78+39, 296)-Net over F₅ — Constructive and digital

Digital (78, 117, 296)-net over F₅, using

1 times m-reduction [i] based on digital (78, 118, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 59, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(78, 78+39, 546)-Net over F₅ — Digital

Digital (78, 117, 546)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+39, 36676)-Net in Base 5 — Upper bound on s

There is no (78, 117, 36677)-net in base 5, because

1 times m-reduction [i] would yield (78, 116, 36677)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1203 981992 891387 101842 896218 151765 982069 741715 739328 450724 006406 350226 380272 816525 > 5¹¹⁶ [i]