MinT - Best Known (53, 53+27, s)-Nets in Base 9

Best Known (53, 53+27, s)-Nets in Base 9

(53, 53+27, 448)-Net over F₉ — Constructive and digital

Digital (53, 80, 448)-net over F₉, using

trace code for nets [i] based on digital (13, 40, 224)-net over F₈₁, using
- net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]

(53, 53+27, 1151)-Net over F₉ — Digital

Digital (53, 80, 1151)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+27, 445827)-Net in Base 9 — Upper bound on s

There is no (53, 80, 445828)-net in base 9, because

1 times m-reduction [i] would yield (53, 79, 445828)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2427 512652 539494 505580 404404 471384 980016 980248 200154 717272 966551 488716 447905 > 9⁷⁹ [i]