MinT - Best Known (153−45, 153, s)-Nets in Base 4

Best Known (153−45, 153, s)-Nets in Base 4

(153−45, 153, 384)-Net over F₄ — Constructive and digital

Digital (108, 153, 384)-net over F₄, using

t-expansion [i] based on digital (107, 153, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 51, 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]

(153−45, 153, 725)-Net over F₄ — Digital

Digital (108, 153, 725)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−45, 153, 43575)-Net in Base 4 — Upper bound on s

There is no (108, 153, 43576)-net in base 4, because

1 times m-reduction [i] would yield (108, 152, 43576)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 32 602559 995886 551004 461142 799928 323990 882312 171255 523323 437732 474887 473118 382335 315588 769281 > 4¹⁵² [i]