MinT - Best Known (142−55, 142, s)-Nets in Base 9

Best Known (142−55, 142, s)-Nets in Base 9

(142−55, 142, 740)-Net over F₉ — Constructive and digital

Digital (87, 142, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 71, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(142−55, 142, 861)-Net over F₉ — Digital

Digital (87, 142, 861)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−55, 142, 131379)-Net in Base 9 — Upper bound on s

There is no (87, 142, 131380)-net in base 9, because

1 times m-reduction [i] would yield (87, 141, 131380)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 353 344365 515082 416239 340321 376410 967142 043891 695042 733551 394347 377149 664806 841400 509433 967470 221348 509222 875226 986760 354434 547674 743649 > 9¹⁴¹ [i]