MinT - Best Known (149−56, 149, s)-Nets in Base 9

Best Known (149−56, 149, s)-Nets in Base 9

(149−56, 149, 740)-Net over F₉ — Constructive and digital

Digital (93, 149, 740)-net over F₉, using

t-expansion [i] based on digital (91, 149, 740)-net over F₉, using
- 1 times m-reduction [i] based on digital (91, 150, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 75, 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]

(149−56, 149, 1051)-Net over F₉ — Digital

Digital (93, 149, 1051)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−56, 149, 168968)-Net in Base 9 — Upper bound on s

There is no (93, 149, 168969)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15212 448002 412566 733483 888035 359914 000932 832005 005174 715618 169669 186220 221184 723367 879512 068642 591705 399715 167930 779403 381873 895777 806006 447201 > 9¹⁴⁹ [i]