MinT - Best Known (252−83, 252, s)-Nets in Base 4

Best Known (252−83, 252, s)-Nets in Base 4

(252−83, 252, 450)-Net over F₄ — Constructive and digital

Digital (169, 252, 450)-net over F₄, using

6 times m-reduction [i] based on digital (169, 258, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 129, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(252−83, 252, 705)-Net over F₄ — Digital

Digital (169, 252, 705)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−83, 252, 26062)-Net in Base 4 — Upper bound on s

There is no (169, 252, 26063)-net in base 4, because

1 times m-reduction [i] would yield (169, 251, 26063)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 107435 819533 850470 060923 068165 680075 749681 266313 159418 906282 024016 811469 436499 533755 656730 396256 756443 198506 128734 125198 252418 472593 862286 658249 028100 > 4²⁵¹ [i]