MinT - Best Known (76, 76+47, s)-Nets in Base 5

Best Known (76, 76+47, s)-Nets in Base 5

(76, 76+47, 252)-Net over F₅ — Constructive and digital

Digital (76, 123, 252)-net over F₅, using

9 times m-reduction [i] based on digital (76, 132, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 66, 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]

(76, 76+47, 321)-Net over F₅ — Digital

Digital (76, 123, 321)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+47, 12005)-Net in Base 5 — Upper bound on s

There is no (76, 123, 12006)-net in base 5, because

1 times m-reduction [i] would yield (76, 122, 12006)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 18 835023 785597 288226 544175 734147 136301 838052 692200 342006 817278 015528 573644 657646 301625 > 5¹²² [i]