MinT - Best Known (167−67, 167, s)-Nets in Base 3

Best Known (167−67, 167, s)-Nets in Base 3

(167−67, 167, 128)-Net over F₃ — Constructive and digital

Digital (100, 167, 128)-net over F₃, using

7 times m-reduction [i] based on digital (100, 174, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 87, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(167−67, 167, 159)-Net over F₃ — Digital

Digital (100, 167, 159)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−67, 167, 1621)-Net in Base 3 — Upper bound on s

There is no (100, 167, 1622)-net in base 3, because

1 times m-reduction [i] would yield (100, 166, 1622)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16 181614 978826 443459 121224 687778 376091 998956 031245 264085 937199 245758 676328 256621 > 3¹⁶⁶ [i]