MinT - Best Known (178−53, 178, s)-Nets in Base 4

Best Known (178−53, 178, s)-Nets in Base 4

(178−53, 178, 384)-Net over F₄ — Constructive and digital

Digital (125, 178, 384)-net over F₄, using

2 times m-reduction [i] based on digital (125, 180, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 60, 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]

(178−53, 178, 777)-Net over F₄ — Digital

Digital (125, 178, 777)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−53, 178, 44116)-Net in Base 4 — Upper bound on s

There is no (125, 178, 44117)-net in base 4, because

1 times m-reduction [i] would yield (125, 177, 44117)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36703 217916 052074 197822 016900 206095 641028 444558 095048 996780 288567 399748 891937 719473 766229 349950 946557 707312 > 4¹⁷⁷ [i]