MinT - Best Known (167, 167+65, s)-Nets in Base 4

Best Known (167, 167+65, s)-Nets in Base 4

(167, 167+65, 531)-Net over F₄ — Constructive and digital

Digital (167, 232, 531)-net over F₄, using

8 times m-reduction [i] based on digital (167, 240, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 80, 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]

(167, 167+65, 1260)-Net over F₄ — Digital

Digital (167, 232, 1260)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 167+65, 94571)-Net in Base 4 — Upper bound on s

There is no (167, 232, 94572)-net in base 4, because

1 times m-reduction [i] would yield (167, 231, 94572)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 911186 585476 792054 641521 806735 644589 692532 764933 403080 595111 366008 765432 569036 833755 753794 551418 678767 430965 813584 940718 010274 450712 019275 > 4²³¹ [i]