MinT - Best Known (147, 147+54, s)-Nets in Base 4

Best Known (147, 147+54, s)-Nets in Base 4

(147, 147+54, 531)-Net over F₄ — Constructive and digital

Digital (147, 201, 531)-net over F₄, using

9 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]

(147, 147+54, 576)-Net in Base 4 — Constructive

(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]

(147, 147+54, 1344)-Net over F₄ — Digital

Digital (147, 201, 1344)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+54, 110459)-Net in Base 4 — Upper bound on s

There is no (147, 201, 110460)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 331470 709976 256716 528276 238250 960438 841422 657492 612196 576683 209719 013347 845721 356781 473999 650300 203115 846946 703051 528673 > 4²⁰¹ [i]