MinT - Best Known (128, 192, s)-Nets in Base 4

Best Known (128, 192, s)-Nets in Base 4

(128, 192, 195)-Net over F₄ — Constructive and digital

Digital (128, 192, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 64, 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]

(128, 192, 240)-Net in Base 4 — Constructive

(128, 192, 240)-net in base 4, using

2 times m-reduction [i] based on (128, 194, 240)-net in base 4, using
- trace code for nets [i] based on (31, 97, 120)-net in base 16, using
  - 3 times m-reduction [i] based on (31, 100, 120)-net in base 16, using
    - base change [i] based on digital (11, 80, 120)-net over F₃₂, using
      - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
        a function field by SÃ©mirat [i]

(128, 192, 531)-Net over F₄ — Digital

Digital (128, 192, 531)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 192, 17436)-Net in Base 4 — Upper bound on s

There is no (128, 192, 17437)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 39 412355 323777 451453 330754 253919 783126 686031 418815 408742 230690 089187 989439 464524 031573 140421 787185 511157 011357 140000 > 4¹⁹² [i]