MinT - Best Known (134−63, 134, s)-Nets in Base 9

Best Known (134−63, 134, s)-Nets in Base 9

(134−63, 134, 300)-Net over F₉ — Constructive and digital

Digital (71, 134, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 67, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(134−63, 134, 328)-Net over F₉ — Digital

Digital (71, 134, 328)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−63, 134, 19254)-Net in Base 9 — Upper bound on s

There is no (71, 134, 19255)-net in base 9, because

1 times m-reduction [i] would yield (71, 133, 19255)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 218720 090428 185385 574668 350181 545958 491479 546156 608331 963073 617347 265661 112607 263905 356245 480826 388424 725952 075225 253538 928201 > 9¹³³ [i]