MinT - Best Known (58, 58+36, s)-Nets in Base 9

Best Known (58, 58+36, s)-Nets in Base 9

(58, 58+36, 344)-Net over F₉ — Constructive and digital

Digital (58, 94, 344)-net over F₉, using

8 times m-reduction [i] based on digital (58, 102, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 51, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(58, 58+36, 653)-Net over F₉ — Digital

Digital (58, 94, 653)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+36, 90835)-Net in Base 9 — Upper bound on s

There is no (58, 94, 90836)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 499859 357683 100755 024318 520450 102078 446302 140704 984029 206088 092486 945562 517286 065114 288065 > 9⁹⁴ [i]