MinT - Best Known (67−22, 67, s)-Nets in Base 5

Best Known (67−22, 67, s)-Nets in Base 5

(67−22, 67, 252)-Net over F₅ — Constructive and digital

Digital (45, 67, 252)-net over F₅, using

3 times m-reduction [i] based on digital (45, 70, 252)-net over F₅, using
- trace code for nets [i] based on 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]

(67−22, 67, 379)-Net over F₅ — Digital

Digital (45, 67, 379)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(67−22, 67, 22190)-Net in Base 5 — Upper bound on s

There is no (45, 67, 22191)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 67782 517395 693539 087024 734816 444441 734703 160725 > 5⁶⁷ [i]