MinT - Best Known (182, 257, s)-Nets in Base 4

Best Known (182, 257, s)-Nets in Base 4

(182, 257, 531)-Net over F₄ — Constructive and digital

Digital (182, 257, 531)-net over F₄, using

t-expansion [i] based on digital (179, 257, 531)-net over F₄, using
- 1 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]

(182, 257, 1154)-Net over F₄ — Digital

Digital (182, 257, 1154)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(182, 257, 71484)-Net in Base 4 — Upper bound on s

There is no (182, 257, 71485)-net in base 4, because

1 times m-reduction [i] would yield (182, 256, 71485)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13412 743830 787603 606408 483267 847511 471068 459654 357578 547069 372004 491046 536524 525843 098910 225180 037166 195241 693321 869572 302885 337653 814167 554155 772754 128700 > 4²⁵⁶ [i]