MinT - Best Known (161−32, 161, s)-Nets in Base 4

Best Known (161−32, 161, s)-Nets in Base 4

(161−32, 161, 1062)-Net over F₄ — Constructive and digital

Digital (129, 161, 1062)-net over F₄, using

4¹ times duplication [i] based on digital (128, 160, 1062)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (16, 32, 34)-net over F₄, using
    - trace code for nets [i] based on digital (0, 16, 17)-net over F₁₆, using
      - net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
        the rational function field F₁₆(x) [i]
        Niederreiter sequence [i]
  2. digital (96, 128, 1028)-net over F₄, using
    - trace code for nets [i] based on digital (0, 32, 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]

(161−32, 161, 5558)-Net over F₄ — Digital

Digital (129, 161, 5558)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(161−32, 161, 2592053)-Net in Base 4 — Upper bound on s

There is no (129, 161, 2592054)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 543967 807986 833247 440480 134919 736201 212842 840156 629421 776596 136843 661152 681863 520037 757944 748867 > 4¹⁶¹ [i]