MinT - Best Known (88, 88+57, s)-Nets in Base 9

Best Known (88, 88+57, s)-Nets in Base 9

(88, 88+57, 448)-Net over F₉ — Constructive and digital

Digital (88, 145, 448)-net over F₉, using

5 times m-reduction [i] based on digital (88, 150, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 75, 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]

(88, 88+57, 811)-Net over F₉ — Digital

Digital (88, 145, 811)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+57, 114125)-Net in Base 9 — Upper bound on s

There is no (88, 145, 114126)-net in base 9, because

1 times m-reduction [i] would yield (88, 144, 114126)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 257607 589078 430689 557185 162456 754572 350258 728322 951856 951674 026364 304904 930303 598788 039493 023062 190791 666005 717811 247173 386259 120051 947201 > 9¹⁴⁴ [i]