MinT - Best Known (103−39, 103, s)-Nets in Base 9

Best Known (103−39, 103, s)-Nets in Base 9

(103−39, 103, 344)-Net over F₉ — Constructive and digital

Digital (64, 103, 344)-net over F₉, using

11 times m-reduction [i] based on digital (64, 114, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 57, 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]

(103−39, 103, 744)-Net over F₉ — Digital

Digital (64, 103, 744)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(103−39, 103, 131481)-Net in Base 9 — Upper bound on s

There is no (64, 103, 131482)-net in base 9, because

1 times m-reduction [i] would yield (64, 102, 131482)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21 517345 285270 818632 299246 304808 337765 167467 187522 647127 144680 690849 450293 311161 820703 579004 467377 > 9¹⁰² [i]