MinT - Best Known (39, 39+60, s)-Nets in Base 9

Best Known (39, 39+60, s)-Nets in Base 9

(39, 39+60, 81)-Net over F₉ — Constructive and digital

Digital (39, 99, 81)-net over F₉, using

t-expansion [i] based on digital (32, 99, 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]

(39, 39+60, 140)-Net over F₉ — Digital

Digital (39, 99, 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]

(39, 39+60, 2103)-Net in Base 9 — Upper bound on s

There is no (39, 99, 2104)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29692 819968 520604 507484 821684 631189 540238 995521 521421 731975 117235 562549 702084 639843 136741 331329 > 9⁹⁹ [i]