MinT - Best Known (134−51, 134, s)-Nets in Base 5

Best Known (134−51, 134, s)-Nets in Base 5

(134−51, 134, 252)-Net over F₅ — Constructive and digital

Digital (83, 134, 252)-net over F₅, using

12 times m-reduction [i] based on digital (83, 146, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 73, 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]

(134−51, 134, 350)-Net over F₅ — Digital

Digital (83, 134, 350)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−51, 134, 13288)-Net in Base 5 — Upper bound on s

There is no (83, 134, 13289)-net in base 5, because

1 times m-reduction [i] would yield (83, 133, 13289)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 918 448196 385093 341159 951906 348993 906283 436453 566816 160144 648313 034908 385891 119617 513756 202949 > 5¹³³ [i]