MinT - Best Known (201−50, 201, s)-Nets in Base 4

Best Known (201−50, 201, s)-Nets in Base 4

(201−50, 201, 1028)-Net over F₄ — Constructive and digital

Digital (151, 201, 1028)-net over F₄, using

4¹ times duplication [i] based on digital (150, 200, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 50, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(201−50, 201, 1903)-Net over F₄ — Digital

Digital (151, 201, 1903)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(201−50, 201, 234979)-Net in Base 4 — Upper bound on s

There is no (151, 201, 234980)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 329935 626787 808353 080841 988874 875381 582096 922236 962848 681423 233237 058477 702118 801580 031406 466051 156526 789933 102643 068756 > 4²⁰¹ [i]