MinT - Best Known (218−66, 218, s)-Nets in Base 4

Best Known (218−66, 218, s)-Nets in Base 4

(218−66, 218, 450)-Net over F₄ — Constructive and digital

Digital (152, 218, 450)-net over F₄, using

6 times m-reduction [i] based on digital (152, 224, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 112, 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]

(218−66, 218, 860)-Net over F₄ — Digital

Digital (152, 218, 860)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−66, 218, 41609)-Net in Base 4 — Upper bound on s

There is no (152, 218, 41610)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 177473 948129 616240 275179 366596 720194 261829 103191 694854 581020 245620 157644 271541 148398 413456 431039 917642 189567 215831 734881 400711 954212 > 4²¹⁸ [i]