MinT - Best Known (82, 182, s)-Nets in Base 3

Best Known (82, 182, s)-Nets in Base 3

(82, 182, 57)-Net over F₃ — Constructive and digital

Digital (82, 182, 57)-net over F₃, using

net from sequence [i] based on digital (82, 56)-sequence over F₃, using
- base reduction for sequences [i] based on digital (13, 56)-sequence over F₉, using
  - s-reduction based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(82, 182, 84)-Net over F₃ — Digital

Digital (82, 182, 84)-net over F₃, using

t-expansion [i] based on digital (71, 182, 84)-net over F₃, using
- net from sequence [i] based on digital (71, 83)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(82, 182, 483)-Net in Base 3 — Upper bound on s

There is no (82, 182, 484)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 708 911457 874830 387423 451755 188832 720568 623729 410568 839837 835673 893030 720890 378500 402041 > 3¹⁸² [i]