MinT - Best Known (139−51, 139, s)-Nets in Base 9

Best Known (139−51, 139, s)-Nets in Base 9

(139−51, 139, 740)-Net over F₉ — Constructive and digital

Digital (88, 139, 740)-net over F₉, using

5 times m-reduction [i] based on digital (88, 144, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 72, 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]

(139−51, 139, 1120)-Net over F₉ — Digital

Digital (88, 139, 1120)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−51, 139, 235465)-Net in Base 9 — Upper bound on s

There is no (88, 139, 235466)-net in base 9, because

1 times m-reduction [i] would yield (88, 138, 235466)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 484737 403006 127727 589451 269397 870776 075561 117415 569191 029728 660446 849510 371243 509232 669147 063712 266055 774849 110504 665491 358608 904913 > 9¹³⁸ [i]