MinT - Best Known (186−62, 186, s)-Nets in Base 4

Best Known (186−62, 186, s)-Nets in Base 4

(186−62, 186, 195)-Net over F₄ — Constructive and digital

Digital (124, 186, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 62, 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]

(186−62, 186, 240)-Net in Base 4 — Constructive

(124, 186, 240)-net in base 4, using

2 times m-reduction [i] based on (124, 188, 240)-net in base 4, using
- trace code for nets [i] based on (30, 94, 120)-net in base 16, using
  - 1 times m-reduction [i] based on (30, 95, 120)-net in base 16, using
    - base change [i] based on digital (11, 76, 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]

(186−62, 186, 516)-Net over F₄ — Digital

Digital (124, 186, 516)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−62, 186, 16928)-Net in Base 4 — Upper bound on s

There is no (124, 186, 16929)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9625 600299 133636 733664 285126 083549 720595 804049 220001 843640 879582 122220 364990 153750 892493 726075 201944 562503 456160 > 4¹⁸⁶ [i]