MinT - Best Known (44, 111, s)-Nets in Base 9

Best Known (44, 111, s)-Nets in Base 9

(44, 111, 81)-Net over F₉ — Constructive and digital

Digital (44, 111, 81)-net over F₉, using

t-expansion [i] based on digital (32, 111, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(44, 111, 82)-Net in Base 9 — Constructive

(44, 111, 82)-net in base 9, using

base change [i] based on digital (7, 74, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(44, 111, 147)-Net over F₉ — Digital

Digital (44, 111, 147)-net over F₉, using

t-expansion [i] based on digital (43, 111, 147)-net over F₉, using
- net from sequence [i] based on digital (43, 146)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
    - a curve from the manYPoints database [i]

(44, 111, 2474)-Net in Base 9 — Upper bound on s

There is no (44, 111, 2475)-net in base 9, because

1 times m-reduction [i] would yield (44, 110, 2475)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 926 948532 100154 421889 156274 612399 037142 064153 067492 567170 955056 162164 841943 630156 836961 762162 596685 348953 > 9¹¹⁰ [i]