MinT - Best Known (128, 128+48, s)-Nets in Base 4

Best Known (128, 128+48, s)-Nets in Base 4

(128, 128+48, 531)-Net over F₄ — Constructive and digital

Digital (128, 176, 531)-net over F₄, using

t-expansion [i] based on digital (127, 176, 531)-net over F₄, using
- 4 times m-reduction [i] based on digital (127, 180, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 60, 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]

(128, 128+48, 1124)-Net over F₄ — Digital

Digital (128, 176, 1124)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+48, 84966)-Net in Base 4 — Upper bound on s

There is no (128, 176, 84967)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9174 932732 393501 833960 301211 000844 938142 770321 608532 051842 284336 616513 250499 379744 247195 780952 594122 190396 > 4¹⁷⁶ [i]