MinT - Best Known (168−67, 168, s)-Nets in Base 4

Best Known (168−67, 168, s)-Nets in Base 4

(168−67, 168, 130)-Net over F₄ — Constructive and digital

Digital (101, 168, 130)-net over F₄, using

22 times m-reduction [i] based on digital (101, 190, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 95, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(168−67, 168, 254)-Net over F₄ — Digital

Digital (101, 168, 254)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−67, 168, 4859)-Net in Base 4 — Upper bound on s

There is no (101, 168, 4860)-net in base 4, because

1 times m-reduction [i] would yield (101, 167, 4860)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35038 489321 541021 375414 682066 023329 519599 731527 210606 795267 365743 652400 901658 048366 178167 848251 138117 > 4¹⁶⁷ [i]