MinT - Best Known (228−69, 228, s)-Nets in Base 4

Best Known (228−69, 228, s)-Nets in Base 4

(228−69, 228, 531)-Net over F₄ — Constructive and digital

Digital (159, 228, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 76, 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]

(228−69, 228, 895)-Net over F₄ — Digital

Digital (159, 228, 895)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−69, 228, 47177)-Net in Base 4 — Upper bound on s

There is no (159, 228, 47178)-net in base 4, because

1 times m-reduction [i] would yield (159, 227, 47178)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46538 118641 527053 928281 050941 922737 297934 553089 671835 713959 068362 223601 767121 935176 063440 939952 671998 731880 085505 942972 039476 442871 412040 > 4²²⁷ [i]