MinT - Best Known (166−64, 166, s)-Nets in Base 3

Best Known (166−64, 166, s)-Nets in Base 3

(166−64, 166, 148)-Net over F₃ — Constructive and digital

Digital (102, 166, 148)-net over F₃, using

4 times m-reduction [i] based on digital (102, 170, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 85, 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]

(166−64, 166, 177)-Net over F₃ — Digital

Digital (102, 166, 177)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−64, 166, 1878)-Net in Base 3 — Upper bound on s

There is no (102, 166, 1879)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16 140950 454748 059557 371683 517574 097535 140457 523350 759937 717593 458481 922642 044353 > 3¹⁶⁶ [i]