MinT - Best Known (110, 164, s)-Nets in Base 4

Best Known (110, 164, s)-Nets in Base 4

(110, 164, 195)-Net over F₄ — Constructive and digital

Digital (110, 164, 195)-net over F₄, using

1 times m-reduction [i] based on digital (110, 165, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 55, 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]

(110, 164, 240)-Net in Base 4 — Constructive

(110, 164, 240)-net in base 4, using

trace code for nets [i] based on (28, 82, 120)-net in base 16, using
- 3 times m-reduction [i] based on (28, 85, 120)-net in base 16, using
  - base change [i] based on digital (11, 68, 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]

(110, 164, 486)-Net over F₄ — Digital

Digital (110, 164, 486)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(110, 164, 16506)-Net in Base 4 — Upper bound on s

There is no (110, 164, 16507)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 546 941334 288273 108962 767482 702832 473731 522923 697980 737013 899534 273726 461728 167521 494057 460723 108980 > 4¹⁶⁴ [i]