MinT - Best Known (142−73, 142, s)-Nets in Base 9

Best Known (142−73, 142, s)-Nets in Base 9

(142−73, 142, 165)-Net over F₉ — Constructive and digital

Digital (69, 142, 165)-net over F₉, using

t-expansion [i] based on digital (64, 142, 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]

(142−73, 142, 235)-Net over F₉ — Digital

Digital (69, 142, 235)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−73, 142, 9730)-Net in Base 9 — Upper bound on s

There is no (69, 142, 9731)-net in base 9, because

1 times m-reduction [i] would yield (69, 141, 9731)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 354 533309 536750 132623 154644 795013 581015 400741 149024 075561 538613 869706 011600 414832 617201 020667 953727 302222 504414 564792 045032 223931 839585 > 9¹⁴¹ [i]