MinT - Best Known (33−15, 33, s)-Nets in Base 9

Best Known (33−15, 33, s)-Nets in Base 9

(33−15, 33, 200)-Net over F₉ — Constructive and digital

Digital (18, 33, 200)-net over F₉, using

1 times m-reduction [i] based on digital (18, 34, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 17, 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]

(33−15, 33, 9725)-Net in Base 9 — Upper bound on s

There is no (18, 33, 9726)-net in base 9, because

1 times m-reduction [i] would yield (18, 32, 9726)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 435184 281124 315489 049000 350929 > 9³² [i]