MinT - Best Known (176−81, 176, s)-Nets in Base 4

Best Known (176−81, 176, s)-Nets in Base 4

(176−81, 176, 130)-Net over F₄ — Constructive and digital

Digital (95, 176, 130)-net over F₄, using

2 times m-reduction [i] based on digital (95, 178, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 89, 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]

(176−81, 176, 167)-Net over F₄ — Digital

Digital (95, 176, 167)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−81, 176, 2230)-Net in Base 4 — Upper bound on s

There is no (95, 176, 2231)-net in base 4, because

1 times m-reduction [i] would yield (95, 175, 2231)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2320 560310 568155 946452 993158 717175 790936 862526 252721 387301 022657 849246 987490 127582 203075 362722 655306 507078 > 4¹⁷⁵ [i]