MinT - Best Known (134−58, 134, s)-Nets in Base 5

Best Known (134−58, 134, s)-Nets in Base 5

(134−58, 134, 208)-Net over F₅ — Constructive and digital

Digital (76, 134, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 67, 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]

(134−58, 134, 218)-Net over F₅ — Digital

Digital (76, 134, 218)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−58, 134, 4930)-Net in Base 5 — Upper bound on s

There is no (76, 134, 4931)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4596 129256 831935 209755 521843 947720 820342 989494 523296 126585 943508 822916 482783 766160 082003 716765 > 5¹³⁴ [i]