MinT - Best Known (92, 138, s)-Nets in Base 4

Best Known (92, 138, s)-Nets in Base 4

(92, 138, 195)-Net over F₄ — Constructive and digital

Digital (92, 138, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 46, 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]

(92, 138, 208)-Net in Base 4 — Constructive

(92, 138, 208)-net in base 4, using

trace code for nets [i] based on (23, 69, 104)-net in base 16, using
- 1 times m-reduction [i] based on (23, 70, 104)-net in base 16, using
  - base change [i] based on digital (9, 56, 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]

(92, 138, 402)-Net over F₄ — Digital

Digital (92, 138, 402)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(92, 138, 12854)-Net in Base 4 — Upper bound on s

There is no (92, 138, 12855)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 121461 407916 427905 300205 107404 093988 317826 878859 869023 958446 981868 378570 124639 131236 > 4¹³⁸ [i]