MinT - Best Known (70, 70+63, s)-Nets in Base 5

Best Known (70, 70+63, s)-Nets in Base 5

(70, 70+63, 104)-Net over F₅ — Constructive and digital

Digital (70, 133, 104)-net over F₅, using

1 times m-reduction [i] based on digital (70, 134, 104)-net over F₅, using
- trace code for nets [i] based on digital (3, 67, 52)-net over F₂₅, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by GarcÃa and Quoos [i]

(70, 70+63, 158)-Net over F₅ — Digital

Digital (70, 133, 158)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+63, 2916)-Net in Base 5 — Upper bound on s

There is no (70, 133, 2917)-net in base 5, because

1 times m-reduction [i] would yield (70, 132, 2917)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 184 574943 151815 297476 210579 638090 622583 405473 980385 005869 120702 878212 520143 620680 688847 458077 > 5¹³² [i]