MinT - Best Known (182−49, 182, s)-Nets in Base 4

Best Known (182−49, 182, s)-Nets in Base 4

(182−49, 182, 531)-Net over F₄ — Constructive and digital

Digital (133, 182, 531)-net over F₄, using

7 times m-reduction [i] based on digital (133, 189, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 63, 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]

(182−49, 182, 1222)-Net over F₄ — Digital

Digital (133, 182, 1222)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−49, 182, 113423)-Net in Base 4 — Upper bound on s

There is no (133, 182, 113424)-net in base 4, because

1 times m-reduction [i] would yield (133, 181, 113424)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 395396 954600 398258 150487 411753 812755 968235 956486 938067 307918 298416 127124 632905 665554 240381 411751 275837 654864 > 4¹⁸¹ [i]