MinT - Best Known (111−32, 111, s)-Nets in Base 4

Best Known (111−32, 111, s)-Nets in Base 4

(111−32, 111, 384)-Net over F₄ — Constructive and digital

Digital (79, 111, 384)-net over F₄, using

trace code for nets [i] based on digital (5, 37, 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]

(111−32, 111, 608)-Net over F₄ — Digital

Digital (79, 111, 608)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−32, 111, 34044)-Net in Base 4 — Upper bound on s

There is no (79, 111, 34045)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 742055 955548 949448 305410 533691 204935 125489 551099 833695 702448 025497 > 4¹¹¹ [i]