MinT - Best Known (109−30, 109, s)-Nets in Base 5

Best Known (109−30, 109, s)-Nets in Base 5

(109−30, 109, 296)-Net over F₅ — Constructive and digital

Digital (79, 109, 296)-net over F₅, using

11 times m-reduction [i] based on digital (79, 120, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 60, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(109−30, 109, 1251)-Net over F₅ — Digital

Digital (79, 109, 1251)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−30, 109, 192692)-Net in Base 5 — Upper bound on s

There is no (79, 109, 192693)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 15408 229643 097704 645515 805971 893443 594030 856497 968735 158584 048608 558094 096029 > 5¹⁰⁹ [i]