MinT - Best Known (77, 77+41, s)-Nets in Base 5

Best Known (77, 77+41, s)-Nets in Base 5

(77, 77+41, 252)-Net over F₅ — Constructive and digital

Digital (77, 118, 252)-net over F₅, using

16 times m-reduction [i] based on digital (77, 134, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 67, 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, 77+41, 457)-Net over F₅ — Digital

Digital (77, 118, 457)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+41, 25466)-Net in Base 5 — Upper bound on s

There is no (77, 118, 25467)-net in base 5, because

1 times m-reduction [i] would yield (77, 117, 25467)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6019 688067 301678 264608 433547 964044 782294 894856 505667 010219 891357 044822 832115 803185 > 5¹¹⁷ [i]