MinT - Best Known (142−36, 142, s)-Nets in Base 4

Best Known (142−36, 142, s)-Nets in Base 4

(142−36, 142, 531)-Net over F₄ — Constructive and digital

Digital (106, 142, 531)-net over F₄, using

t-expansion [i] based on digital (105, 142, 531)-net over F₄, using
- 5 times m-reduction [i] based on digital (105, 147, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 49, 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]

(142−36, 142, 576)-Net in Base 4 — Constructive

(106, 142, 576)-net in base 4, using

2 times m-reduction [i] based on (106, 144, 576)-net in base 4, using
- trace code for nets [i] based on (10, 48, 192)-net in base 64, using
  - 1 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]

(142−36, 142, 1302)-Net over F₄ — Digital

Digital (106, 142, 1302)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−36, 142, 141432)-Net in Base 4 — Upper bound on s

There is no (106, 142, 141433)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31 085402 870351 474633 888087 566078 126543 863204 091755 347438 158441 478680 863749 983386 923980 > 4¹⁴² [i]