MinT - Best Known (166−38, 166, s)-Nets in Base 3

Best Known (166−38, 166, s)-Nets in Base 3

(166−38, 166, 464)-Net over F₃ — Constructive and digital

Digital (128, 166, 464)-net over F₃, using

2 times m-reduction [i] based on digital (128, 168, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 42, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(166−38, 166, 1031)-Net over F₃ — Digital

Digital (128, 166, 1031)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−38, 166, 58422)-Net in Base 3 — Upper bound on s

There is no (128, 166, 58423)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15 928712 813351 177918 568706 523827 095043 589369 049806 257334 780501 121972 480349 755579 > 3¹⁶⁶ [i]