MinT - Best Known (241−71, 241, s)-Nets in Base 4

Best Known (241−71, 241, s)-Nets in Base 4

(241−71, 241, 531)-Net over F₄ — Constructive and digital

Digital (170, 241, 531)-net over F₄, using

t-expansion [i] based on digital (169, 241, 531)-net over F₄, using
- 2 times m-reduction [i] based on digital (169, 243, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 81, 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]

(241−71, 241, 1049)-Net over F₄ — Digital

Digital (170, 241, 1049)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−71, 241, 62280)-Net in Base 4 — Upper bound on s

There is no (170, 241, 62281)-net in base 4, because

1 times m-reduction [i] would yield (170, 240, 62281)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 122123 012223 066937 874955 849944 108102 629654 733817 344957 898294 421139 913419 174439 001386 254275 556794 101982 674246 253707 631777 456053 682479 785295 679120 > 4²⁴⁰ [i]