MinT - Best Known (108, 147, s)-Nets in Base 4

Best Known (108, 147, s)-Nets in Base 4

(108, 147, 531)-Net over F₄ — Constructive and digital

Digital (108, 147, 531)-net over F₄, using

t-expansion [i] based on digital (107, 147, 531)-net over F₄, using
- 3 times m-reduction [i] based on digital (107, 150, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 50, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(108, 147, 576)-Net in Base 4 — Constructive

(108, 147, 576)-net in base 4, using

trace code for nets [i] based on (10, 49, 192)-net in base 64, using
- base change [i] based on digital (3, 42, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]

(108, 147, 1087)-Net over F₄ — Digital

Digital (108, 147, 1087)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 147, 111786)-Net in Base 4 — Upper bound on s

There is no (108, 147, 111787)-net in base 4, because

1 times m-reduction [i] would yield (108, 146, 111787)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7957 481540 135615 185437 789449 542029 764167 927983 549122 991523 777324 160329 516270 316102 733640 > 4¹⁴⁶ [i]