MinT - Best Known (40, 40+103, s)-Nets in Base 9

Best Known (40, 40+103, s)-Nets in Base 9

(40, 40+103, 81)-Net over F₉ — Constructive and digital

Digital (40, 143, 81)-net over F₉, using

t-expansion [i] based on digital (32, 143, 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]

(40, 40+103, 140)-Net over F₉ — Digital

Digital (40, 143, 140)-net over F₉, using

t-expansion [i] based on digital (39, 143, 140)-net over F₉, using
- net from sequence [i] based on digital (39, 139)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
    - a curve from the manYPoints database [i]

(40, 40+103, 1095)-Net in Base 9 — Upper bound on s

There is no (40, 143, 1096)-net in base 9, because

1 times m-reduction [i] would yield (40, 142, 1096)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3292 105735 604452 035620 949078 954828 981858 014525 279136 986092 393545 736629 890325 537595 706613 985239 291842 469654 937302 467654 418507 717564 231105 > 9¹⁴² [i]