MinT - Best Known (145−42, 145, s)-Nets in Base 4

Best Known (145−42, 145, s)-Nets in Base 4

(145−42, 145, 384)-Net over F₄ — Constructive and digital

Digital (103, 145, 384)-net over F₄, using

2 times m-reduction [i] based on digital (103, 147, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 49, 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]

(145−42, 145, 744)-Net over F₄ — Digital

Digital (103, 145, 744)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−42, 145, 41521)-Net in Base 4 — Upper bound on s

There is no (103, 145, 41522)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1989 658900 855993 229448 460660 888095 570474 094245 703868 068480 534778 927133 272132 957474 838712 > 4¹⁴⁵ [i]