MinT - Best Known (32, 32+108, s)-Nets in Base 9

Best Known (32, 32+108, s)-Nets in Base 9

(32, 32+108, 81)-Net over F₉ — Constructive and digital

Digital (32, 140, 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]

(32, 32+108, 120)-Net over F₉ — Digital

Digital (32, 140, 120)-net over F₉, using

t-expansion [i] based on digital (31, 140, 120)-net over F₉, using
- net from sequence [i] based on digital (31, 119)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 31 and N(F) ≥ 120, using
    - a curve from the manYPoints database [i]

(32, 32+108, 747)-Net in Base 9 — Upper bound on s

There is no (32, 140, 748)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 994575 845826 254971 041238 300359 243279 213073 645684 496841 507228 143521 550178 308280 472372 075639 604346 301996 125278 663626 175629 658492 461761 > 9¹⁴⁰ [i]