MinT - Best Known (77, 77+44, s)-Nets in Base 5

Best Known (77, 77+44, s)-Nets in Base 5

(77, 77+44, 252)-Net over F₅ — Constructive and digital

Digital (77, 121, 252)-net over F₅, using

13 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+44, 385)-Net over F₅ — Digital

Digital (77, 121, 385)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+44, 15801)-Net in Base 5 — Upper bound on s

There is no (77, 121, 15802)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 766034 203372 756348 330870 949957 913634 912769 854863 668252 899449 611927 479783 069017 879425 > 5¹²¹ [i]