MinT - Best Known (80, 119, s)-Nets in Base 4

Best Known (80, 119, s)-Nets in Base 4

(80, 119, 195)-Net over F₄ — Constructive and digital

Digital (80, 119, 195)-net over F₄, using

1 times m-reduction [i] based on digital (80, 120, 195)-net over F₄, using
- trace code for nets [i] based on digital (0, 40, 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]

(80, 119, 196)-Net in Base 4 — Constructive

(80, 119, 196)-net in base 4, using

t-expansion [i] based on (79, 119, 196)-net in base 4, using
- 1 times m-reduction [i] based on (79, 120, 196)-net in base 4, using
  - trace code for nets [i] based on (19, 60, 98)-net in base 16, using
    - base change [i] based on digital (7, 48, 98)-net over F₃₂, using
      - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
        a function field by SÃ©mirat [i]

(80, 119, 382)-Net over F₄ — Digital

Digital (80, 119, 382)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 119, 14479)-Net in Base 4 — Upper bound on s

There is no (80, 119, 14480)-net in base 4, because

1 times m-reduction [i] would yield (80, 118, 14480)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 110545 629187 240251 318687 287110 162960 796757 095285 266103 944863 203442 324424 > 4¹¹⁸ [i]