MinT - Best Known (56, 56+38, s)-Nets in Base 9

Best Known (56, 56+38, s)-Nets in Base 9

(56, 56+38, 344)-Net over F₉ — Constructive and digital

Digital (56, 94, 344)-net over F₉, using

4 times m-reduction [i] based on digital (56, 98, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 49, 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]

(56, 56+38, 502)-Net over F₉ — Digital

Digital (56, 94, 502)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+38, 52121)-Net in Base 9 — Upper bound on s

There is no (56, 94, 52122)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 499822 720618 272566 980360 932016 261035 798913 425367 303986 632517 564060 382644 284513 713227 344049 > 9⁹⁴ [i]