MinT - Best Known (144−73, 144, s)-Nets in Base 9

Best Known (144−73, 144, s)-Nets in Base 9

(144−73, 144, 165)-Net over F₉ — Constructive and digital

Digital (71, 144, 165)-net over F₉, using

t-expansion [i] based on digital (64, 144, 165)-net over F₉, using
- net from sequence [i] based on digital (64, 164)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 64 and N(F) ≥ 165, using
    - T₄ from the second tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(144−73, 144, 252)-Net over F₉ — Digital

Digital (71, 144, 252)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−73, 144, 10996)-Net in Base 9 — Upper bound on s

There is no (71, 144, 10997)-net in base 9, because

1 times m-reduction [i] would yield (71, 143, 10997)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 28694 894451 891764 212476 816391 796200 843207 208126 506527 567621 374913 259740 892583 334035 907728 732136 813138 962633 608377 091340 460336 442263 642657 > 9¹⁴³ [i]