MinT - Best Known (69, 109, s)-Nets in Base 5

Best Known (69, 109, s)-Nets in Base 5

(69, 109, 252)-Net over F₅ — Constructive and digital

Digital (69, 109, 252)-net over F₅, using

9 times m-reduction [i] based on digital (69, 118, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 59, 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]

(69, 109, 342)-Net over F₅ — Digital

Digital (69, 109, 342)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 109, 13370)-Net in Base 5 — Upper bound on s

There is no (69, 109, 13371)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 15408 611141 139687 536196 521461 178131 319644 095452 043602 280686 884578 424061 156401 > 5¹⁰⁹ [i]