MinT - Best Known (144−93, 144, s)-Nets in Base 9

Best Known (144−93, 144, s)-Nets in Base 9

(144−93, 144, 81)-Net over F₉ — Constructive and digital

Digital (51, 144, 81)-net over F₉, using

t-expansion [i] based on digital (32, 144, 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]

(144−93, 144, 182)-Net over F₉ — Digital

Digital (51, 144, 182)-net over F₉, using

t-expansion [i] based on digital (50, 144, 182)-net over F₉, using
- net from sequence [i] based on digital (50, 181)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
    - a curve from the manYPoints database [i]

(144−93, 144, 2054)-Net in Base 9 — Upper bound on s

There is no (51, 144, 2055)-net in base 9, because

1 times m-reduction [i] would yield (51, 143, 2055)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29013 744002 537631 132603 666232 790339 672380 953103 394948 141602 597157 097117 354749 101305 260988 239084 327519 885763 114592 042559 740999 218468 214545 > 9¹⁴³ [i]