MinT - Best Known (63, 63+39, s)-Nets in Base 9

Best Known (63, 63+39, s)-Nets in Base 9

(63, 63+39, 344)-Net over F₉ — Constructive and digital

Digital (63, 102, 344)-net over F₉, using

10 times m-reduction [i] based on digital (63, 112, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 56, 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]

(63, 63+39, 703)-Net over F₉ — Digital

Digital (63, 102, 703)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+39, 117121)-Net in Base 9 — Upper bound on s

There is no (63, 102, 117122)-net in base 9, because

1 times m-reduction [i] would yield (63, 101, 117122)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 390823 906211 937878 281406 395250 839854 034548 953455 464996 037472 970316 455596 060795 702405 372032 712049 > 9¹⁰¹ [i]