MinT - Best Known (44−23, 44, s)-Nets in Base 9

Best Known (44−23, 44, s)-Nets in Base 9

(44−23, 44, 74)-Net over F₉ — Constructive and digital

Digital (21, 44, 74)-net over F₉, using

t-expansion [i] based on digital (17, 44, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(44−23, 44, 76)-Net in Base 9 — Constructive

(21, 44, 76)-net in base 9, using

1 times m-reduction [i] based on (21, 45, 76)-net in base 9, using
- base change [i] based on digital (6, 30, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(44−23, 44, 89)-Net over F₉ — Digital

Digital (21, 44, 89)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(44−23, 44, 3290)-Net in Base 9 — Upper bound on s

There is no (21, 44, 3291)-net in base 9, because

1 times m-reduction [i] would yield (21, 43, 3291)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 107815 275562 914281 183117 913157 553024 134345 > 9⁴³ [i]