MinT - Best Known (104, 104+36, s)-Nets in Base 4

Best Known (104, 104+36, s)-Nets in Base 4

(104, 104+36, 531)-Net over F₄ — Constructive and digital

Digital (104, 140, 531)-net over F₄, using

t-expansion [i] based on digital (103, 140, 531)-net over F₄, using
- 4 times m-reduction [i] based on digital (103, 144, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 48, 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]

(104, 104+36, 576)-Net in Base 4 — Constructive

(104, 140, 576)-net in base 4, using

1 times m-reduction [i] based on (104, 141, 576)-net in base 4, using
- trace code for nets [i] based on (10, 47, 192)-net in base 64, using
  - 2 times m-reduction [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]

(104, 104+36, 1204)-Net over F₄ — Digital

Digital (104, 140, 1204)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(104, 104+36, 121239)-Net in Base 4 — Upper bound on s

There is no (104, 140, 121240)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 942688 161116 599107 358441 156860 247983 627941 545317 695613 221750 202126 348527 534076 909465 > 4¹⁴⁰ [i]