MinT - Best Known (147−29, 147, s)-Nets in Base 4

Best Known (147−29, 147, s)-Nets in Base 4

(147−29, 147, 1076)-Net over F₄ — Constructive and digital

Digital (118, 147, 1076)-net over F₄, using

4¹ times duplication [i] based on digital (117, 146, 1076)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (16, 30, 48)-net over F₄, using
    - trace code for nets [i] based on digital (1, 15, 24)-net over F₁₆, using
      - net from sequence [i] based on digital (1, 23)-sequence over F₁₆, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
        a function field by SÃ©mirat [i]
  2. digital (87, 116, 1028)-net over F₄, using
    - trace code for nets [i] based on digital (0, 29, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]

(147−29, 147, 5467)-Net over F₄ — Digital

Digital (118, 147, 5467)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−29, 147, 3827902)-Net in Base 4 — Upper bound on s

There is no (118, 147, 3827903)-net in base 4, because

1 times m-reduction [i] would yield (118, 146, 3827903)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7957 192935 154681 547554 187258 581779 513679 832266 468007 189710 217791 960249 816240 484813 421871 > 4¹⁴⁶ [i]