MinT - Best Known (70, 70+62, s)-Nets in Base 9

Best Known (70, 70+62, s)-Nets in Base 9

(70, 70+62, 300)-Net over F₉ — Constructive and digital

Digital (70, 132, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 66, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(70, 70+62, 325)-Net over F₉ — Digital

Digital (70, 132, 325)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+62, 17935)-Net in Base 9 — Upper bound on s

There is no (70, 132, 17936)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 912887 779196 387242 813162 031417 895077 249622 150232 507161 699177 547714 790142 395636 607204 404250 588831 779739 500898 078642 369289 666945 > 9¹³² [i]