MinT - Best Known (166−76, 166, s)-Nets in Base 4

Best Known (166−76, 166, s)-Nets in Base 4

(166−76, 166, 130)-Net over F₄ — Constructive and digital

Digital (90, 166, 130)-net over F₄, using

2 times m-reduction [i] based on digital (90, 168, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 84, 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]

(166−76, 166, 161)-Net over F₄ — Digital

Digital (90, 166, 161)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−76, 166, 2105)-Net in Base 4 — Upper bound on s

There is no (90, 166, 2106)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8802 584343 765511 261996 741255 897169 686966 319206 889781 134865 109781 954616 687536 234645 980637 001995 510740 > 4¹⁶⁶ [i]