MinT - Best Known (82, 82+39, s)-Nets in Base 3

Best Known (82, 82+39, s)-Nets in Base 3

(82, 82+39, 148)-Net over F₃ — Constructive and digital

Digital (82, 121, 148)-net over F₃, using

9 times m-reduction [i] based on digital (82, 130, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 65, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(82, 82+39, 232)-Net over F₃ — Digital

Digital (82, 121, 232)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+39, 4070)-Net in Base 3 — Upper bound on s

There is no (82, 121, 4071)-net in base 3, because

1 times m-reduction [i] would yield (82, 120, 4071)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1803 594195 128003 051999 776819 828561 856760 437612 971338 078331 > 3¹²⁰ [i]