MinT - Best Known (126−42, 126, s)-Nets in Base 9

Best Known (126−42, 126, s)-Nets in Base 9

(126−42, 126, 740)-Net over F₉ — Constructive and digital

Digital (84, 126, 740)-net over F₉, using

10 times m-reduction [i] based on digital (84, 136, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 68, 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]

(126−42, 126, 1748)-Net over F₉ — Digital

Digital (84, 126, 1748)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−42, 126, 576564)-Net in Base 9 — Upper bound on s

There is no (84, 126, 576565)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 716166 012464 197257 927097 093086 136212 757322 408804 840021 733271 344542 009324 663100 201867 823025 817908 794297 476168 384693 872201 > 9¹²⁶ [i]