MinT - Best Known (205−50, 205, s)-Nets in Base 4

Best Known (205−50, 205, s)-Nets in Base 4

(205−50, 205, 1032)-Net over F₄ — Constructive and digital

Digital (155, 205, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (154, 204, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 51, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(205−50, 205, 2128)-Net over F₄ — Digital

Digital (155, 205, 2128)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−50, 205, 293336)-Net in Base 4 — Upper bound on s

There is no (155, 205, 293337)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2644 291920 878948 987033 538877 369926 914000 979967 248203 146236 505616 778423 403969 797771 200129 403869 546347 595031 601895 320704 603988 > 4²⁰⁵ [i]