MinT - Best Known (151−30, 151, s)-Nets in Base 4

Best Known (151−30, 151, s)-Nets in Base 4

(151−30, 151, 1062)-Net over F₄ — Constructive and digital

Digital (121, 151, 1062)-net over F₄, using

4¹ times duplication [i] based on digital (120, 150, 1062)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 30, 34)-net over F₄, using
    - trace code for nets [i] based on digital (0, 15, 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 (90, 120, 1028)-net over F₄, using
    - trace code for nets [i] based on digital (0, 30, 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]

(151−30, 151, 5321)-Net over F₄ — Digital

Digital (121, 151, 5321)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(151−30, 151, 2462524)-Net in Base 4 — Upper bound on s

There is no (121, 151, 2462525)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 148181 194441 772921 830678 344806 314098 336212 612471 345471 059830 188277 560486 612848 438324 934096 > 4¹⁵¹ [i]