MinT - Best Known (70, 70+35, s)-Nets in Base 5

Best Known (70, 70+35, s)-Nets in Base 5

(70, 70+35, 252)-Net over F₅ — Constructive and digital

Digital (70, 105, 252)-net over F₅, using

15 times m-reduction [i] based on digital (70, 120, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 60, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(70, 70+35, 504)-Net over F₅ — Digital

Digital (70, 105, 504)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+35, 33867)-Net in Base 5 — Upper bound on s

There is no (70, 105, 33868)-net in base 5, because

1 times m-reduction [i] would yield (70, 104, 33868)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4 932229 700026 060291 964976 458262 535157 282029 645359 445025 324264 292171 349809 > 5¹⁰⁴ [i]