MinT - Best Known (65, 65+35, s)-Nets in Base 5

Best Known (65, 65+35, s)-Nets in Base 5

(65, 65+35, 252)-Net over F₅ — Constructive and digital

Digital (65, 100, 252)-net over F₅, using

10 times m-reduction [i] based on digital (65, 110, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 55, 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]

(65, 65+35, 391)-Net over F₅ — Digital

Digital (65, 100, 391)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+35, 21091)-Net in Base 5 — Upper bound on s

There is no (65, 100, 21092)-net in base 5, because

1 times m-reduction [i] would yield (65, 99, 21092)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1578 480143 181256 306334 088796 017075 060911 632987 124088 510242 743128 759185 > 5⁹⁹ [i]