MinT - Best Known (82, 82+40, s)-Nets in Base 9

Best Known (82, 82+40, s)-Nets in Base 9

(82, 82+40, 740)-Net over F₉ — Constructive and digital

Digital (82, 122, 740)-net over F₉, using

10 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, 82+40, 1879)-Net over F₉ — Digital

Digital (82, 122, 1879)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+40, 687207)-Net in Base 9 — Upper bound on s

There is no (82, 122, 687208)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 261 571802 832768 833344 741928 369795 894603 876533 837859 499615 472389 667652 185659 902617 677081 428519 862492 703960 335880 894209 > 9¹²² [i]