MinT - Best Known (46, 111, s)-Nets in Base 9

Best Known (46, 111, s)-Nets in Base 9

(46, 111, 81)-Net over F₉ — Constructive and digital

Digital (46, 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]

(46, 111, 88)-Net in Base 9 — Constructive

(46, 111, 88)-net in base 9, using

base change [i] based on digital (9, 74, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(46, 111, 162)-Net over F₉ — Digital

Digital (46, 111, 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, 111, 3028)-Net in Base 9 — Upper bound on s

There is no (46, 111, 3029)-net in base 9, because

1 times m-reduction [i] would yield (46, 110, 3029)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 931 748261 438773 635192 089532 435240 630049 652631 179659 973022 440461 256939 458122 536938 505858 785146 667326 404865 > 9¹¹⁰ [i]