MinT - Best Known (82, 82+43, s)-Nets in Base 9

Best Known (82, 82+43, s)-Nets in Base 9

(82, 82+43, 740)-Net over F₉ — Constructive and digital

Digital (82, 125, 740)-net over F₉, using

7 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+43, 1449)-Net over F₉ — Digital

Digital (82, 125, 1449)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+43, 467698)-Net in Base 9 — Upper bound on s

There is no (82, 125, 467699)-net in base 9, because

1 times m-reduction [i] would yield (82, 124, 467699)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21187 868400 403237 406454 321327 002789 798705 016390 672351 278702 053325 186039 390221 350574 958047 881540 206563 439950 124525 921913 > 9¹²⁴ [i]