MinT - Best Known (144−65, 144, s)-Nets in Base 9

Best Known (144−65, 144, s)-Nets in Base 9

(144−65, 144, 344)-Net over F₉ — Constructive and digital

Digital (79, 144, 344)-net over F₉, using

trace code for nets [i] based on digital (7, 72, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

(144−65, 144, 416)-Net over F₉ — Digital

Digital (79, 144, 416)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−65, 144, 29361)-Net in Base 9 — Upper bound on s

There is no (79, 144, 29362)-net in base 9, because

1 times m-reduction [i] would yield (79, 143, 29362)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 28646 585979 772231 974738 808632 616322 555290 475101 541993 888730 765309 484566 815593 936837 404812 496811 596273 398558 362757 440002 523819 898019 628545 > 9¹⁴³ [i]