MinT - Best Known (134−55, 134, s)-Nets in Base 5

Best Known (134−55, 134, s)-Nets in Base 5

(134−55, 134, 252)-Net over F₅ — Constructive and digital

Digital (79, 134, 252)-net over F₅, using

4 times m-reduction [i] based on digital (79, 138, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 69, 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]

(134−55, 134, 265)-Net over F₅ — Digital

Digital (79, 134, 265)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−55, 134, 7555)-Net in Base 5 — Upper bound on s

There is no (79, 134, 7556)-net in base 5, because

1 times m-reduction [i] would yield (79, 133, 7556)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 918 545206 330552 909969 429725 983010 350587 474237 967634 686589 439388 911023 613362 268596 625577 061905 > 5¹³³ [i]