MinT - Best Known (248−69, 248, s)-Nets in Base 4

Best Known (248−69, 248, s)-Nets in Base 4

(248−69, 248, 531)-Net over F₄ — Constructive and digital

Digital (179, 248, 531)-net over F₄, using

10 times m-reduction [i] based on 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]

(248−69, 248, 1376)-Net over F₄ — Digital

Digital (179, 248, 1376)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−69, 248, 106666)-Net in Base 4 — Upper bound on s

There is no (179, 248, 106667)-net in base 4, because

1 times m-reduction [i] would yield (179, 247, 106667)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51148 500773 558097 982338 257397 134494 058711 806984 973190 523714 478945 007334 133333 918864 415526 657237 139332 504771 371269 536202 571881 052642 159665 882522 701789 > 4²⁴⁷ [i]