MinT - Best Known (126−51, 126, s)-Nets in Base 5

Best Known (126−51, 126, s)-Nets in Base 5

(126−51, 126, 252)-Net over F₅ — Constructive and digital

Digital (75, 126, 252)-net over F₅, using

4 times m-reduction [i] based on digital (75, 130, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 65, 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]

(126−51, 126, 264)-Net over F₅ — Digital

Digital (75, 126, 264)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−51, 126, 7932)-Net in Base 5 — Upper bound on s

There is no (75, 126, 7933)-net in base 5, because

1 times m-reduction [i] would yield (75, 125, 7933)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2353 524789 961185 751139 836225 529077 061582 250283 537549 050711 761818 891317 610982 555184 919573 > 5¹²⁵ [i]