MinT - Best Known (70, 70+62, s)-Nets in Base 5

Best Known (70, 70+62, s)-Nets in Base 5

(70, 70+62, 132)-Net over F₅ — Constructive and digital

Digital (70, 132, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 66, 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]

(70, 70+62, 162)-Net over F₅ — Digital

Digital (70, 132, 162)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+62, 2916)-Net in Base 5 — Upper bound on s

There is no (70, 132, 2917)-net in base 5, because

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]