MinT - Best Known (31−14, 31, s)-Nets in Base 9

Best Known (31−14, 31, s)-Nets in Base 9

(31−14, 31, 200)-Net over F₉ — Constructive and digital

Digital (17, 31, 200)-net over F₉, using

1 times m-reduction [i] based on digital (17, 32, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 16, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(31−14, 31, 7104)-Net in Base 9 — Upper bound on s

There is no (17, 31, 7105)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 381773 007545 249125 508683 912569 > 9³¹ [i]