MinT - Best Known (137−49, 137, s)-Nets in Base 9

Best Known (137−49, 137, s)-Nets in Base 9

(137−49, 137, 740)-Net over F₉ — Constructive and digital

Digital (88, 137, 740)-net over F₉, using

7 times m-reduction [i] based on digital (88, 144, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 72, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(137−49, 137, 1264)-Net over F₉ — Digital

Digital (88, 137, 1264)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−49, 137, 313059)-Net in Base 9 — Upper bound on s

There is no (88, 137, 313060)-net in base 9, because

1 times m-reduction [i] would yield (88, 136, 313060)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 5984 098131 218895 376315 468153 347807 839941 635875 336015 531315 376840 493530 912555 620614 621808 826551 295814 956018 403941 401082 672546 983169 > 9¹³⁶ [i]