MinT - Best Known (202−54, 202, s)-Nets in Base 4

Best Known (202−54, 202, s)-Nets in Base 4

(202−54, 202, 531)-Net over F₄ — Constructive and digital

Digital (148, 202, 531)-net over F₄, using

t-expansion [i] based on digital (147, 202, 531)-net over F₄, using
- 8 times m-reduction [i] based on digital (147, 210, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 70, 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]

(202−54, 202, 576)-Net in Base 4 — Constructive

(148, 202, 576)-net in base 4, using

4¹ times duplication [i] based on (147, 201, 576)-net in base 4, using
- trace code for nets [i] based on (13, 67, 192)-net in base 64, using
  - 3 times m-reduction [i] based on (13, 70, 192)-net in base 64, using
    - base change [i] based on digital (3, 60, 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]

(202−54, 202, 1379)-Net over F₄ — Digital

Digital (148, 202, 1379)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−54, 202, 116279)-Net in Base 4 — Upper bound on s

There is no (148, 202, 116280)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 318530 839800 095713 290017 125802 646166 184401 842414 202642 120759 832646 004049 893959 857338 638970 272919 523723 256376 741483 043972 > 4²⁰² [i]