MinT - Best Known (166−63, 166, s)-Nets in Base 4

Best Known (166−63, 166, s)-Nets in Base 4

(166−63, 166, 130)-Net over F₄ — Constructive and digital

Digital (103, 166, 130)-net over F₄, using

28 times m-reduction [i] based on digital (103, 194, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 97, 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]

(166−63, 166, 298)-Net over F₄ — Digital

Digital (103, 166, 298)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−63, 166, 6603)-Net in Base 4 — Upper bound on s

There is no (103, 166, 6604)-net in base 4, because

1 times m-reduction [i] would yield (103, 165, 6604)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2193 952748 272697 338447 033879 671107 650946 571360 934212 548361 171739 789158 105589 662077 897840 690916 019792 > 4¹⁶⁵ [i]