MinT - Best Known (129−61, 129, s)-Nets in Base 4

Best Known (129−61, 129, s)-Nets in Base 4

(129−61, 129, 76)-Net over F₄ — Constructive and digital

Digital (68, 129, 76)-net over F₄, using

1 times m-reduction [i] based on digital (68, 130, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 65, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(129−61, 129, 118)-Net over F₄ — Digital

Digital (68, 129, 118)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−61, 129, 1463)-Net in Base 4 — Upper bound on s

There is no (68, 129, 1464)-net in base 4, because

1 times m-reduction [i] would yield (68, 128, 1464)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 117786 923622 393487 947520 985107 629515 666371 276236 014204 357899 681902 788328 269020 > 4¹²⁸ [i]