MinT - Best Known (33, 33+110, s)-Nets in Base 9

Best Known (33, 33+110, s)-Nets in Base 9

(33, 33+110, 81)-Net over F₉ — Constructive and digital

Digital (33, 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]

(33, 33+110, 128)-Net over F₉ — Digital

Digital (33, 143, 128)-net over F₉, using

net from sequence [i] based on digital (33, 127)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
  - a curve from the manYPoints database [i]

(33, 33+110, 773)-Net in Base 9 — Upper bound on s

There is no (33, 143, 774)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 28716 806809 495523 330857 139102 837536 273296 417182 702913 589818 102338 388221 881699 527036 185998 207263 740069 514255 918556 322371 254433 118675 334801 > 9¹⁴³ [i]