MinT - Best Known (62, 62+48, s)-Nets in Base 25

Best Known (62, 62+48, s)-Nets in Base 25

(62, 62+48, 326)-Net over F₂₅ — Constructive and digital

Digital (62, 110, 326)-net over F₂₅, using

t-expansion [i] based on digital (60, 110, 326)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 35, 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]
  2. digital (25, 75, 200)-net over F₂₅, using
    - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
        a function field by GarcÃa and Quoos [i]

(62, 62+48, 1455)-Net over F₂₅ — Digital

Digital (62, 110, 1455)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+48, 1043209)-Net in Base 25 — Upper bound on s

There is no (62, 110, 1043210)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 5934 864620 980093 124294 547689 753853 996951 807798 553335 948317 320685 114801 111878 870182 915083 017569 265948 772455 207725 851961 173271 835956 678192 255164 057817 538945 > 25¹¹⁰ [i]