MinT - Best Known (260−70, 260, s)-Nets in Base 4

Best Known (260−70, 260, s)-Nets in Base 4

(260−70, 260, 531)-Net over F₄ — Constructive and digital

Digital (190, 260, 531)-net over F₄, using

4² times duplication [i] based on digital (188, 258, 531)-net over F₄, using
- t-expansion [i] based on digital (179, 258, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 86, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(260−70, 260, 576)-Net in Base 4 — Constructive

(190, 260, 576)-net in base 4, using

4² times duplication [i] based on (188, 258, 576)-net in base 4, using
- trace code for nets [i] based on (16, 86, 192)-net in base 64, using
  - 5 times m-reduction [i] based on (16, 91, 192)-net in base 64, using
    - base change [i] based on digital (3, 78, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(260−70, 260, 1661)-Net over F₄ — Digital

Digital (190, 260, 1661)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−70, 260, 137561)-Net in Base 4 — Upper bound on s

There is no (190, 260, 137562)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 432615 320753 414179 097088 766521 089942 306604 088732 066238 099251 372034 953758 470152 473777 724364 463735 962828 898918 794950 123861 788068 800253 914188 216186 874018 367560 > 4²⁶⁰ [i]