MinT - Best Known (46, 139, s)-Nets in Base 9

Best Known (46, 139, s)-Nets in Base 9

(46, 139, 81)-Net over F₉ — Constructive and digital

Digital (46, 139, 81)-net over F₉, using

t-expansion [i] based on digital (32, 139, 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, 139, 162)-Net over F₉ — Digital

Digital (46, 139, 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, 139, 1611)-Net in Base 9 — Upper bound on s

There is no (46, 139, 1612)-net in base 9, because

1 times m-reduction [i] would yield (46, 138, 1612)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 484962 775363 166858 175919 642985 911030 725962 760389 835362 927769 582036 685439 268654 256165 572976 849379 446806 702193 449793 102181 278636 846017 > 9¹³⁸ [i]