MinT - Best Known (57, 57+43, s)-Nets in Base 9

Best Known (57, 57+43, s)-Nets in Base 9

(57, 57+43, 344)-Net over F₉ — Constructive and digital

Digital (57, 100, 344)-net over F₉, using

trace code for nets [i] based on digital (7, 50, 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]

(57, 57+43, 386)-Net over F₉ — Digital

Digital (57, 100, 386)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+43, 34183)-Net in Base 9 — Upper bound on s

There is no (57, 100, 34184)-net in base 9, because

1 times m-reduction [i] would yield (57, 99, 34184)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29525 251560 936537 508203 202808 902949 812511 599886 691903 175019 658473 605205 438225 448918 429752 419137 > 9⁹⁹ [i]