MinT - Best Known (70, 70+30, s)-Nets in Base 5

Best Known (70, 70+30, s)-Nets in Base 5

(70, 70+30, 296)-Net over F₅ — Constructive and digital

Digital (70, 100, 296)-net over F₅, using

2 times m-reduction [i] based on digital (70, 102, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 51, 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]

(70, 70+30, 765)-Net over F₅ — Digital

Digital (70, 100, 765)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+30, 73357)-Net in Base 5 — Upper bound on s

There is no (70, 100, 73358)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7889 818401 739623 398239 380435 409961 090261 987227 719835 046580 655056 621145 > 5¹⁰⁰ [i]