MinT - Best Known (144−107, 144, s)-Nets in Base 9

Best Known (144−107, 144, s)-Nets in Base 9

(144−107, 144, 81)-Net over F₉ — Constructive and digital

Digital (37, 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]

(144−107, 144, 128)-Net over F₉ — Digital

Digital (37, 144, 128)-net over F₉, using

t-expansion [i] based on digital (33, 144, 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]

(144−107, 144, 934)-Net in Base 9 — Upper bound on s

There is no (37, 144, 935)-net in base 9, because

1 times m-reduction [i] would yield (37, 143, 935)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29361 489131 538800 025878 091591 556331 024447 022849 015843 578529 927386 778377 802480 755938 602625 508871 228831 157932 785859 143932 697074 744191 091353 > 9¹⁴³ [i]