MinT - Best Known (111−34, 111, s)-Nets in Base 4

Best Known (111−34, 111, s)-Nets in Base 4

(111−34, 111, 312)-Net over F₄ — Constructive and digital

Digital (77, 111, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 37, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(111−34, 111, 478)-Net over F₄ — Digital

Digital (77, 111, 478)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−34, 111, 20400)-Net in Base 4 — Upper bound on s

There is no (77, 111, 20401)-net in base 4, because

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]