MinT - Best Known (153, 153+55, s)-Nets in Base 4

Best Known (153, 153+55, s)-Nets in Base 4

(153, 153+55, 531)-Net over F₄ — Constructive and digital

Digital (153, 208, 531)-net over F₄, using

11 times m-reduction [i] based on digital (153, 219, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 73, 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]

(153, 153+55, 576)-Net in Base 4 — Constructive

(153, 208, 576)-net in base 4, using

2 times m-reduction [i] based on (153, 210, 576)-net in base 4, using
- trace code for nets [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]

(153, 153+55, 1484)-Net over F₄ — Digital

Digital (153, 208, 1484)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(153, 153+55, 150319)-Net in Base 4 — Upper bound on s

There is no (153, 208, 150320)-net in base 4, because

1 times m-reduction [i] would yield (153, 207, 150320)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42311 626540 719921 405980 149873 349280 662566 710623 573350 160397 964672 793827 197300 286056 086960 737602 944189 413415 627805 970409 360590 > 4²⁰⁷ [i]