MinT - Best Known (205−51, 205, s)-Nets in Base 4

Best Known (205−51, 205, s)-Nets in Base 4

(205−51, 205, 1028)-Net over F₄ — Constructive and digital

Digital (154, 205, 1028)-net over F₄, using

4¹ times duplication [i] based on digital (153, 204, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 51, 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]

(205−51, 205, 1935)-Net over F₄ — Digital

Digital (154, 205, 1935)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−51, 205, 277512)-Net in Base 4 — Upper bound on s

There is no (154, 205, 277513)-net in base 4, because

1 times m-reduction [i] would yield (154, 204, 277513)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 661 095898 056984 518471 889663 206907 451725 113202 156465 186266 622905 844369 074373 849083 037448 156506 885899 032059 458060 777464 632064 > 4²⁰⁴ [i]