MinT - Best Known (62, 62+41, s)-Nets in Base 5

Best Known (62, 62+41, s)-Nets in Base 5

(62, 62+41, 252)-Net over F₅ — Constructive and digital

Digital (62, 103, 252)-net over F₅, using

1 times m-reduction [i] based on digital (62, 104, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 52, 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]

(62, 62+41, 7606)-Net in Base 5 — Upper bound on s

There is no (62, 103, 7607)-net in base 5, because

1 times m-reduction [i] would yield (62, 102, 7607)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 197639 130709 559855 250770 749131 475547 845422 956005 288748 971941 115202 667185 > 5¹⁰² [i]