MinT - Best Known (77−28, 77, s)-Nets in Base 5

Best Known (77−28, 77, s)-Nets in Base 5

(77−28, 77, 252)-Net over F₅ — Constructive and digital

Digital (49, 77, 252)-net over F₅, using

1 times m-reduction [i] based on digital (49, 78, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 39, 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]

(77−28, 77, 276)-Net over F₅ — Digital

Digital (49, 77, 276)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(77−28, 77, 10551)-Net in Base 5 — Upper bound on s

There is no (49, 77, 10552)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 662027 178012 721251 981793 574915 266440 107845 539237 425025 > 5⁷⁷ [i]