MinT - Best Known (173, 173+60, s)-Nets in Base 4

Best Known (173, 173+60, s)-Nets in Base 4

(173, 173+60, 541)-Net over F₄ — Constructive and digital

Digital (173, 233, 541)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (2, 32, 10)-net over F₄, using
  - net from sequence [i] based on digital (2, 9)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 2 and N(F) ≥ 10, using
      - an explicitly constructive algebraic function field [i]
2. digital (141, 201, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 67, 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]

(173, 173+60, 648)-Net in Base 4 — Constructive

(173, 233, 648)-net in base 4, using

4² times duplication [i] based on (171, 231, 648)-net in base 4, using
- t-expansion [i] based on (170, 231, 648)-net in base 4, using
  - trace code for nets [i] based on (16, 77, 216)-net in base 64, using
    - base change [i] based on digital (5, 66, 216)-net over F₁₂₈, using
      - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(173, 173+60, 1844)-Net over F₄ — Digital

Digital (173, 233, 1844)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(173, 173+60, 190375)-Net in Base 4 — Upper bound on s

There is no (173, 233, 190376)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 190 554855 529603 859868 685374 852949 686612 247968 090543 142995 581820 850865 575597 520439 566226 482323 472472 779270 083658 901965 028958 856842 847854 594156 > 4²³³ [i]