MinT - Best Known (46, 46+66, s)-Nets in Base 9

Best Known (46, 46+66, s)-Nets in Base 9

(46, 46+66, 81)-Net over F₉ — Constructive and digital

Digital (46, 112, 81)-net over F₉, using

t-expansion [i] based on digital (32, 112, 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]

(46, 46+66, 84)-Net in Base 9 — Constructive

(46, 112, 84)-net in base 9, using

2 times m-reduction [i] based on (46, 114, 84)-net in base 9, using
- base change [i] based on digital (8, 76, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(46, 46+66, 162)-Net over F₉ — Digital

Digital (46, 112, 162)-net over F₉, using

net from sequence [i] based on digital (46, 161)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
  - a curve from the manYPoints database [i]

(46, 46+66, 2830)-Net in Base 9 — Upper bound on s

There is no (46, 112, 2831)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 75615 383253 929489 309524 312088 657800 947949 339109 204993 725298 369639 618957 209028 638992 758472 655456 203715 528569 > 9¹¹² [i]