MinT - Best Known (165, 234, s)-Nets in Base 4

Best Known (165, 234, s)-Nets in Base 4

(165, 234, 531)-Net over F₄ — Constructive and digital

Digital (165, 234, 531)-net over F₄, using

3 times m-reduction [i] based on digital (165, 237, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 79, 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]

(165, 234, 1019)-Net over F₄ — Digital

Digital (165, 234, 1019)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 234, 60260)-Net in Base 4 — Upper bound on s

There is no (165, 234, 60261)-net in base 4, because

1 times m-reduction [i] would yield (165, 233, 60261)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 190 550793 297989 889677 268438 425833 615307 869974 879889 534198 283854 082571 225466 663936 275752 859611 096745 629094 295079 929223 680170 469822 412319 650650 > 4²³³ [i]