MinT - Best Known (108, 162, s)-Nets in Base 4

Best Known (108, 162, s)-Nets in Base 4

(108, 162, 195)-Net over F₄ — Constructive and digital

Digital (108, 162, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 54, 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]

(108, 162, 208)-Net in Base 4 — Constructive

(108, 162, 208)-net in base 4, using

2 times m-reduction [i] based on (108, 164, 208)-net in base 4, using
- trace code for nets [i] based on (26, 82, 104)-net in base 16, using
  - 3 times m-reduction [i] based on (26, 85, 104)-net in base 16, using
    - base change [i] based on digital (9, 68, 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]

(108, 162, 459)-Net over F₄ — Digital

Digital (108, 162, 459)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 162, 14893)-Net in Base 4 — Upper bound on s

There is no (108, 162, 14894)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 34 189707 883325 821152 621790 541820 047681 278103 024857 247657 288593 372180 186235 766351 943065 022990 718500 > 4¹⁶² [i]