MinT - Best Known (139−58, 139, s)-Nets in Base 5

Best Known (139−58, 139, s)-Nets in Base 5

(139−58, 139, 252)-Net over F₅ — Constructive and digital

Digital (81, 139, 252)-net over F₅, using

3 times m-reduction [i] based on digital (81, 142, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 71, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(139−58, 139, 257)-Net over F₅ — Digital

Digital (81, 139, 257)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−58, 139, 6514)-Net in Base 5 — Upper bound on s

There is no (81, 139, 6515)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 14 377529 748675 701068 795781 891432 687114 678472 515526 976260 464927 742555 952694 180498 673402 094276 323165 > 5¹³⁹ [i]