MinT - Best Known (205−40, 205, s)-Nets in Base 4

Best Known (205−40, 205, s)-Nets in Base 4

(205−40, 205, 1539)-Net over F₄ — Constructive and digital

Digital (165, 205, 1539)-net over F₄, using

4¹ times duplication [i] based on digital (164, 204, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 68, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(205−40, 205, 7518)-Net over F₄ — Digital

Digital (165, 205, 7518)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−40, 205, 4104858)-Net in Base 4 — Upper bound on s

There is no (165, 205, 4104859)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2644 232044 916148 216193 971168 559431 534656 310539 907922 933503 610166 487893 412822 095139 738726 373233 671030 975057 286394 485465 475654 > 4²⁰⁵ [i]