MinT - Best Known (92, 92+56, s)-Nets in Base 5

Best Known (92, 92+56, s)-Nets in Base 5

(92, 92+56, 252)-Net over F₅ — Constructive and digital

Digital (92, 148, 252)-net over F₅, using

t-expansion [i] based on digital (85, 148, 252)-net over F₅, using
- 2 times m-reduction [i] based on digital (85, 150, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 75, 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]

(92, 92+56, 389)-Net over F₅ — Digital

Digital (92, 148, 389)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(92, 92+56, 13959)-Net in Base 5 — Upper bound on s

There is no (92, 148, 13960)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 065014 453800 382242 576073 060843 021449 348001 112275 474923 953461 082300 261635 047995 364011 183845 687173 139457 > 5¹⁴⁸ [i]