MinT - Best Known (166, 166+63, s)-Nets in Base 3

Best Known (166, 166+63, s)-Nets in Base 3

(166, 166+63, 288)-Net over F₃ — Constructive and digital

Digital (166, 229, 288)-net over F₃, using

t-expansion [i] based on digital (165, 229, 288)-net over F₃, using
- 2 times m-reduction [i] based on digital (165, 231, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 77, 96)-net over F₂₇, using
    - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
        an explicitly constructive algebraic function field [i]

(166, 166+63, 666)-Net over F₃ — Digital

Digital (166, 229, 666)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166, 166+63, 20021)-Net in Base 3 — Upper bound on s

There is no (166, 229, 20022)-net in base 3, because

1 times m-reduction [i] would yield (166, 228, 20022)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 083021 722972 241138 444690 645844 369346 193845 074238 577150 648925 949325 499547 893116 206671 868910 221805 995823 116905 > 3²²⁸ [i]