MinT - Best Known (107, 158, s)-Nets in Base 4

Best Known (107, 158, s)-Nets in Base 4

(107, 158, 240)-Net over F₄ — Constructive and digital

Digital (107, 158, 240)-net over F₄, using

1 times m-reduction [i] based on digital (107, 159, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 53, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(107, 158, 508)-Net over F₄ — Digital

Digital (107, 158, 508)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 158, 20464)-Net in Base 4 — Upper bound on s

There is no (107, 158, 20465)-net in base 4, because

1 times m-reduction [i] would yield (107, 157, 20465)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 33377 779898 732567 305733 406670 260001 802120 117692 232639 526790 268939 736124 557939 440971 153152 109168 > 4¹⁵⁷ [i]