MinT - Best Known (168−82, 168, s)-Nets in Base 4

Best Known (168−82, 168, s)-Nets in Base 4

(168−82, 168, 104)-Net over F₄ — Constructive and digital

Digital (86, 168, 104)-net over F₄, using

t-expansion [i] based on digital (73, 168, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(168−82, 168, 133)-Net over F₄ — Digital

Digital (86, 168, 133)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−82, 168, 1543)-Net in Base 4 — Upper bound on s

There is no (86, 168, 1544)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 142263 708869 168117 720632 944622 252707 641448 101918 879223 373873 751824 977984 892111 910621 359162 012338 300352 > 4¹⁶⁸ [i]