MinT - Best Known (76, 76+28, s)-Nets in Base 4

Best Known (76, 76+28, s)-Nets in Base 4

(76, 76+28, 384)-Net over F₄ — Constructive and digital

Digital (76, 104, 384)-net over F₄, using

t-expansion [i] based on digital (75, 104, 384)-net over F₄, using
- 1 times m-reduction [i] based on digital (75, 105, 384)-net over F₄, using
  - trace code for nets [i] based on digital (5, 35, 128)-net over F₆₄, using
    - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
        a function field by SÃ©mirat [i]

(76, 76+28, 450)-Net in Base 4 — Constructive

(76, 104, 450)-net in base 4, using

1 times m-reduction [i] based on (76, 105, 450)-net in base 4, using
- trace code for nets [i] based on (6, 35, 150)-net in base 64, using
  - base change [i] based on digital (1, 30, 150)-net over F₁₂₈, using
    - net from sequence [i] based on digital (1, 149)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
        a function field by SÃ©mirat [i]

(76, 76+28, 772)-Net over F₄ — Digital

Digital (76, 104, 772)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+28, 59799)-Net in Base 4 — Upper bound on s

There is no (76, 104, 59800)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 411 377907 002105 789041 302219 005320 661846 973189 894606 868827 679606 > 4¹⁰⁴ [i]