MinT - Best Known (173−51, 173, s)-Nets in Base 4

Best Known (173−51, 173, s)-Nets in Base 4

(173−51, 173, 384)-Net over F₄ — Constructive and digital

Digital (122, 173, 384)-net over F₄, using

t-expansion [i] based on digital (121, 173, 384)-net over F₄, using
- 1 times m-reduction [i] based on digital (121, 174, 384)-net over F₄, using
  - trace code for nets [i] based on digital (5, 58, 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]

(173−51, 173, 792)-Net over F₄ — Digital

Digital (122, 173, 792)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−51, 173, 47042)-Net in Base 4 — Upper bound on s

There is no (122, 173, 47043)-net in base 4, because

1 times m-reduction [i] would yield (122, 172, 47043)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35 846932 328432 124166 872978 071906 915966 957975 685644 977819 199654 544017 159709 451063 126658 366845 637057 542192 > 4¹⁷² [i]