MinT - Best Known (79−20, 79, s)-Nets in Base 5

Best Known (79−20, 79, s)-Nets in Base 5

(79−20, 79, 296)-Net over F₅ — Constructive and digital

Digital (59, 79, 296)-net over F₅, using

1 times m-reduction [i] based on digital (59, 80, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 40, 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]

(79−20, 79, 1607)-Net over F₅ — Digital

Digital (59, 79, 1607)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(79−20, 79, 376505)-Net in Base 5 — Upper bound on s

There is no (59, 79, 376506)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 16 543852 074477 396248 868672 846042 892726 485101 310937 097025 > 5⁷⁹ [i]