MinT - Best Known (161, 219, s)-Nets in Base 4

Best Known (161, 219, s)-Nets in Base 4

(161, 219, 531)-Net over F₄ — Constructive and digital

Digital (161, 219, 531)-net over F₄, using

12 times m-reduction [i] based on digital (161, 231, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 77, 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]

(161, 219, 576)-Net in Base 4 — Constructive

(161, 219, 576)-net in base 4, using

t-expansion [i] based on (160, 219, 576)-net in base 4, using
- trace code for nets [i] based on (14, 73, 192)-net in base 64, using
  - 4 times m-reduction [i] based on (14, 77, 192)-net in base 64, using
    - base change [i] based on digital (3, 66, 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]

(161, 219, 1542)-Net over F₄ — Digital

Digital (161, 219, 1542)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(161, 219, 136935)-Net in Base 4 — Upper bound on s

There is no (161, 219, 136936)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 709848 129124 838128 451051 605924 745265 293288 838739 429961 411434 292355 070040 236366 505829 012290 308098 429852 759937 414104 692171 400350 733220 > 4²¹⁹ [i]