MinT - Best Known (128−37, 128, s)-Nets in Base 4

Best Known (128−37, 128, s)-Nets in Base 4

(128−37, 128, 384)-Net over F₄ — Constructive and digital

Digital (91, 128, 384)-net over F₄, using

1 times m-reduction [i] based on digital (91, 129, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 43, 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]

(128−37, 128, 676)-Net over F₄ — Digital

Digital (91, 128, 676)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−37, 128, 44538)-Net in Base 4 — Upper bound on s

There is no (91, 128, 44539)-net in base 4, because

1 times m-reduction [i] would yield (91, 127, 44539)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 28954 370301 423559 964329 898349 482178 187722 586651 270261 653469 540791 126213 068185 > 4¹²⁷ [i]