MinT - Best Known (86, 128, s)-Nets in Base 4

Best Known (86, 128, s)-Nets in Base 4

(86, 128, 195)-Net over F₄ — Constructive and digital

Digital (86, 128, 195)-net over F₄, using

1 times m-reduction [i] based on digital (86, 129, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 43, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(86, 128, 208)-Net in Base 4 — Constructive

(86, 128, 208)-net in base 4, using

trace code for nets [i] based on (22, 64, 104)-net in base 16, using
- 1 times m-reduction [i] based on (22, 65, 104)-net in base 16, using
  - base change [i] based on digital (9, 52, 104)-net over F₃₂, using
    - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(86, 128, 402)-Net over F₄ — Digital

Digital (86, 128, 402)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 128, 13505)-Net in Base 4 — Upper bound on s

There is no (86, 128, 13506)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 115805 951918 190395 096092 704677 606575 612185 825699 019829 556820 241103 396448 245616 > 4¹²⁸ [i]