MinT - Best Known (145−104, 145, s)-Nets in Base 9

Best Known (145−104, 145, s)-Nets in Base 9

(145−104, 145, 81)-Net over F₉ — Constructive and digital

Digital (41, 145, 81)-net over F₉, using

t-expansion [i] based on digital (32, 145, 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]

(145−104, 145, 140)-Net over F₉ — Digital

Digital (41, 145, 140)-net over F₉, using

t-expansion [i] based on digital (39, 145, 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]

(145−104, 145, 1126)-Net in Base 9 — Upper bound on s

There is no (41, 145, 1127)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 406548 333301 385697 911007 324190 048293 116989 247569 205828 621172 689129 832270 291750 705073 719388 132480 477959 748420 535181 723435 040687 737591 529825 > 9¹⁴⁵ [i]