MinT - Best Known (149−69, 149, s)-Nets in Base 9

Best Known (149−69, 149, s)-Nets in Base 9

(149−69, 149, 320)-Net over F₉ — Constructive and digital

Digital (80, 149, 320)-net over F₉, using

1 times m-reduction [i] based on digital (80, 150, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 75, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(149−69, 149, 383)-Net over F₉ — Digital

Digital (80, 149, 383)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−69, 149, 24086)-Net in Base 9 — Upper bound on s

There is no (80, 149, 24087)-net in base 9, because

1 times m-reduction [i] would yield (80, 148, 24087)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1691 292871 763859 583285 634953 457468 455725 565272 597822 410359 108695 735152 378235 490013 143556 220316 965838 321643 781090 668900 589445 608651 599150 017905 > 9¹⁴⁸ [i]