MinT - Best Known (168−68, 168, s)-Nets in Base 4

Best Known (168−68, 168, s)-Nets in Base 4

(168−68, 168, 130)-Net over F₄ — Constructive and digital

Digital (100, 168, 130)-net over F₄, using

20 times m-reduction [i] based on digital (100, 188, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 94, 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]

(168−68, 168, 242)-Net over F₄ — Digital

Digital (100, 168, 242)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−68, 168, 4230)-Net in Base 4 — Upper bound on s

There is no (100, 168, 4231)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 140474 872009 526966 756233 162960 289538 438585 847353 105387 953032 826807 980845 737185 459044 665019 284494 063972 > 4¹⁶⁸ [i]