MinT - Best Known (97, 97+39, s)-Nets in Base 4

Best Known (97, 97+39, s)-Nets in Base 4

(97, 97+39, 384)-Net over F₄ — Constructive and digital

Digital (97, 136, 384)-net over F₄, using

2 times m-reduction [i] based on digital (97, 138, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 46, 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]

(97, 97+39, 734)-Net over F₄ — Digital

Digital (97, 136, 734)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(97, 97+39, 50090)-Net in Base 4 — Upper bound on s

There is no (97, 136, 50091)-net in base 4, because

1 times m-reduction [i] would yield (97, 135, 50091)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1897 443097 968981 871505 133277 486540 565931 506040 702884 410952 536981 084097 541766 118152 > 4¹³⁵ [i]