MinT - Best Known (168−49, 168, s)-Nets in Base 4

Best Known (168−49, 168, s)-Nets in Base 4

(168−49, 168, 531)-Net over F₄ — Constructive and digital

Digital (119, 168, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 56, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(168−49, 168, 810)-Net over F₄ — Digital

Digital (119, 168, 810)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−49, 168, 50513)-Net in Base 4 — Upper bound on s

There is no (119, 168, 50514)-net in base 4, because

1 times m-reduction [i] would yield (119, 167, 50514)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35003 295907 167911 195893 194219 093586 224563 745760 489358 044072 068029 556021 036240 079283 295872 601498 577864 > 4¹⁶⁷ [i]