MinT - Best Known (112−35, 112, s)-Nets in Base 4

Best Known (112−35, 112, s)-Nets in Base 4

(112−35, 112, 240)-Net over F₄ — Constructive and digital

Digital (77, 112, 240)-net over F₄, using

2 times m-reduction [i] based on digital (77, 114, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 38, 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]

(112−35, 112, 442)-Net over F₄ — Digital

Digital (77, 112, 442)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−35, 112, 20400)-Net in Base 4 — Upper bound on s

There is no (77, 112, 20401)-net in base 4, because

1 times m-reduction [i] would yield (77, 111, 20401)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 745443 591046 019234 721431 711445 616469 852048 712974 676108 005102 643004 > 4¹¹¹ [i]