MinT - Best Known (258−79, 258, s)-Nets in Base 4

Best Known (258−79, 258, s)-Nets in Base 4

(258−79, 258, 531)-Net over F₄ — Constructive and digital

Digital (179, 258, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 86, 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]

(258−79, 258, 951)-Net over F₄ — Digital

Digital (179, 258, 951)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(258−79, 258, 47580)-Net in Base 4 — Upper bound on s

There is no (179, 258, 47581)-net in base 4, because

1 times m-reduction [i] would yield (179, 257, 47581)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53633 635080 550934 092856 238515 154585 647404 465935 601723 161223 656614 313915 828295 081704 967757 193924 855035 786500 229663 468421 312490 807696 907771 251551 879869 397040 > 4²⁵⁷ [i]