MinT - Best Known (164−64, 164, s)-Nets in Base 3

Best Known (164−64, 164, s)-Nets in Base 3

(164−64, 164, 148)-Net over F₃ — Constructive and digital

Digital (100, 164, 148)-net over F₃, using

2 times m-reduction [i] based on digital (100, 166, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 83, 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]

(164−64, 164, 169)-Net over F₃ — Digital

Digital (100, 164, 169)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−64, 164, 1751)-Net in Base 3 — Upper bound on s

There is no (100, 164, 1752)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 785392 900606 523598 490112 892401 962746 957638 740438 822961 382134 939354 174830 573569 > 3¹⁶⁴ [i]