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

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

(166−63, 166, 148)-Net over F₃ — Constructive and digital

Digital (103, 166, 148)-net over F₃, using

6 times m-reduction [i] based on digital (103, 172, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 86, 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]

(166−63, 166, 185)-Net over F₃ — Digital

Digital (103, 166, 185)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−63, 166, 2120)-Net in Base 3 — Upper bound on s

There is no (103, 166, 2121)-net in base 3, because

1 times m-reduction [i] would yield (103, 165, 2121)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 379824 979040 287642 179192 530854 437335 677901 202010 965429 083635 110014 588772 053323 > 3¹⁶⁵ [i]