MinT - Best Known (168−69, 168, s)-Nets in Base 4

Best Known (168−69, 168, s)-Nets in Base 4

(168−69, 168, 130)-Net over F₄ — Constructive and digital

Digital (99, 168, 130)-net over F₄, using

18 times m-reduction [i] based on digital (99, 186, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 93, 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]

(168−69, 168, 230)-Net over F₄ — Digital

Digital (99, 168, 230)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−69, 168, 4060)-Net in Base 4 — Upper bound on s

There is no (99, 168, 4061)-net in base 4, because

1 times m-reduction [i] would yield (99, 167, 4061)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35162 210527 511965 119891 050970 818416 138936 953999 388769 039599 039237 265148 623524 525249 801942 731453 949180 > 4¹⁶⁷ [i]