MinT - Best Known (168−51, 168, s)-Nets in Base 4

Best Known (168−51, 168, s)-Nets in Base 4

(168−51, 168, 384)-Net over F₄ — Constructive and digital

Digital (117, 168, 384)-net over F₄, using

trace code for nets [i] based on digital (5, 56, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(168−51, 168, 684)-Net over F₄ — Digital

Digital (117, 168, 684)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−51, 168, 35646)-Net in Base 4 — Upper bound on s

There is no (117, 168, 35647)-net in base 4, because

1 times m-reduction [i] would yield (117, 167, 35647)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35006 633140 718949 919034 879738 828643 265968 817044 501773 834046 244072 798023 561125 973192 676106 993543 923294 > 4¹⁶⁷ [i]