MinT - Best Known (82, 117, s)-Nets in Base 9

Best Known (82, 117, s)-Nets in Base 9

(82, 117, 740)-Net over F₉ — Constructive and digital

Digital (82, 117, 740)-net over F₉, using

15 times m-reduction [i] based on digital (82, 132, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 66, 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]

(82, 117, 3269)-Net over F₉ — Digital

Digital (82, 117, 3269)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 117, 2911759)-Net in Base 9 — Upper bound on s

There is no (82, 117, 2911760)-net in base 9, because

1 times m-reduction [i] would yield (82, 116, 2911760)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 492 188795 248392 583232 696468 577365 516919 735235 377113 328254 428863 152422 615905 949448 590602 940621 887345 877392 328833 > 9¹¹⁶ [i]