MinT - Best Known (179−49, 179, s)-Nets in Base 4

Best Known (179−49, 179, s)-Nets in Base 4

(179−49, 179, 531)-Net over F₄ — Constructive and digital

Digital (130, 179, 531)-net over F₄, using

t-expansion [i] based on digital (129, 179, 531)-net over F₄, using
- 4 times m-reduction [i] based on digital (129, 183, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 61, 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]

(179−49, 179, 1122)-Net over F₄ — Digital

Digital (130, 179, 1122)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(179−49, 179, 95374)-Net in Base 4 — Upper bound on s

There is no (130, 179, 95375)-net in base 4, because

1 times m-reduction [i] would yield (130, 178, 95375)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 146812 941503 874375 431505 509431 399735 979597 394132 238967 121642 336420 788850 153671 881367 885093 321218 105784 429176 > 4¹⁷⁸ [i]