MinT - Best Known (77, 77+30, s)-Nets in Base 5

Best Known (77, 77+30, s)-Nets in Base 5

(77, 77+30, 296)-Net over F₅ — Constructive and digital

Digital (77, 107, 296)-net over F₅, using

9 times m-reduction [i] based on digital (77, 116, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 58, 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]

(77, 77+30, 1121)-Net over F₅ — Digital

Digital (77, 107, 1121)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+30, 155475)-Net in Base 5 — Upper bound on s

There is no (77, 107, 155476)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 616 312586 691135 117110 637469 353517 863896 023583 594580 346116 424356 454465 797585 > 5¹⁰⁷ [i]