MinT - Best Known (73, 73+45, s)-Nets in Base 5

Best Known (73, 73+45, s)-Nets in Base 5

(73, 73+45, 252)-Net over F₅ — Constructive and digital

Digital (73, 118, 252)-net over F₅, using

8 times m-reduction [i] based on digital (73, 126, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 63, 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]

(73, 73+45, 313)-Net over F₅ — Digital

Digital (73, 118, 313)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+45, 11788)-Net in Base 5 — Upper bound on s

There is no (73, 118, 11789)-net in base 5, because

1 times m-reduction [i] would yield (73, 117, 11789)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6025 577866 731245 440522 735313 381637 317779 312901 853171 125308 530925 976717 340255 871305 > 5¹¹⁷ [i]