MinT - Best Known (176−58, 176, s)-Nets in Base 4

Best Known (176−58, 176, s)-Nets in Base 4

(176−58, 176, 195)-Net over F₄ — Constructive and digital

Digital (118, 176, 195)-net over F₄, using

1 times m-reduction [i] based on digital (118, 177, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 59, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(176−58, 176, 240)-Net in Base 4 — Constructive

(118, 176, 240)-net in base 4, using

2 times m-reduction [i] based on (118, 178, 240)-net in base 4, using
- trace code for nets [i] based on (29, 89, 120)-net in base 16, using
  - 1 times m-reduction [i] based on (29, 90, 120)-net in base 16, using
    - base change [i] based on digital (11, 72, 120)-net over F₃₂, using
      - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
        a function field by SÃ©mirat [i]

(176−58, 176, 514)-Net over F₄ — Digital

Digital (118, 176, 514)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−58, 176, 17510)-Net in Base 4 — Upper bound on s

There is no (118, 176, 17511)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9183 255438 410523 141921 798260 143781 313812 321547 627578 572618 917361 775832 833436 156456 005581 246623 329961 845224 > 4¹⁷⁶ [i]