MinT - Best Known (80−35, 80, s)-Nets in Base 5

Best Known (80−35, 80, s)-Nets in Base 5

(80−35, 80, 132)-Net over F₅ — Constructive and digital

Digital (45, 80, 132)-net over F₅, using

2 times m-reduction [i] based on digital (45, 82, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 41, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(80−35, 80, 139)-Net over F₅ — Digital

Digital (45, 80, 139)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(80−35, 80, 3164)-Net in Base 5 — Upper bound on s

There is no (45, 80, 3165)-net in base 5, because

1 times m-reduction [i] would yield (45, 79, 3165)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 16 549510 526701 711350 904233 371342 942081 974989 459589 824565 > 5⁷⁹ [i]