MinT - Best Known (92, 118, s)-Nets in Base 5

Best Known (92, 118, s)-Nets in Base 5

(92, 118, 504)-Net over F₅ — Constructive and digital

Digital (92, 118, 504)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (33, 46, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 23, 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]
2. digital (46, 72, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 36, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(92, 118, 5079)-Net over F₅ — Digital

Digital (92, 118, 5079)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(92, 118, 3132145)-Net in Base 5 — Upper bound on s

There is no (92, 118, 3132146)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 30092 773463 590594 186816 843340 220799 888020 623116 406847 582716 188366 128936 609422 517705 > 5¹¹⁸ [i]