MinT - Best Known (207−51, 207, s)-Nets in Base 4

Best Known (207−51, 207, s)-Nets in Base 4

(207−51, 207, 1028)-Net over F₄ — Constructive and digital

Digital (156, 207, 1028)-net over F₄, using

1 times m-reduction [i] based on digital (156, 208, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 52, 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]

(207−51, 207, 2043)-Net over F₄ — Digital

Digital (156, 207, 2043)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−51, 207, 310063)-Net in Base 4 — Upper bound on s

There is no (156, 207, 310064)-net in base 4, because

1 times m-reduction [i] would yield (156, 206, 310064)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10577 457397 024507 580416 784867 978533 772201 629124 513213 186794 009797 348614 684173 752136 845427 766921 379186 196404 198574 434581 441470 > 4²⁰⁶ [i]