MinT - Best Known (159, 159+53, s)-Nets in Base 4

Best Known (159, 159+53, s)-Nets in Base 4

(159, 159+53, 1028)-Net over F₄ — Constructive and digital

Digital (159, 212, 1028)-net over F₄, using

trace code for nets [i] based on digital (0, 53, 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]

(159, 159+53, 1946)-Net over F₄ — Digital

Digital (159, 212, 1946)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(159, 159+53, 270449)-Net in Base 4 — Upper bound on s

There is no (159, 212, 270450)-net in base 4, because

1 times m-reduction [i] would yield (159, 211, 270450)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 831258 032547 057709 431726 823107 287706 583690 070778 542537 662266 499137 755069 673715 827065 562496 864959 751265 493820 365569 211843 325200 > 4²¹¹ [i]