MinT - Best Known (112, 112+43, s)-Nets in Base 4

Best Known (112, 112+43, s)-Nets in Base 4

(112, 112+43, 531)-Net over F₄ — Constructive and digital

Digital (112, 155, 531)-net over F₄, using

t-expansion [i] based on digital (111, 155, 531)-net over F₄, using
- 1 times m-reduction [i] based on digital (111, 156, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 52, 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]

(112, 112+43, 938)-Net over F₄ — Digital

Digital (112, 155, 938)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+43, 75228)-Net in Base 4 — Upper bound on s

There is no (112, 155, 75229)-net in base 4, because

1 times m-reduction [i] would yield (112, 154, 75229)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 521 619766 642338 023367 454357 279773 282159 362104 349478 619300 308213 310853 636269 727710 509715 794268 > 4¹⁵⁴ [i]