MinT - Best Known (139−117, 139, s)-Nets in Base 9

Best Known (139−117, 139, s)-Nets in Base 9

(139−117, 139, 78)-Net over F₉ — Constructive and digital

Digital (22, 139, 78)-net over F₉, using

net from sequence [i] based on digital (22, 77)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
  - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(139−117, 139, 88)-Net over F₉ — Digital

Digital (22, 139, 88)-net over F₉, using

t-expansion [i] based on digital (21, 139, 88)-net over F₉, using
- net from sequence [i] based on digital (21, 87)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 21 and N(F) ≥ 88, using
    - a curve from the manYPoints database [i]

(139−117, 139, 486)-Net in Base 9 — Upper bound on s

There is no (22, 139, 487)-net in base 9, because

9 times m-reduction [i] would yield (22, 130, 487)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11263 513246 326457 107717 191083 962666 851505 881478 434083 253656 726276 892853 838500 322373 875113 469334 787934 106717 050870 470165 967569 > 9¹³⁰ [i]