MinT - Best Known (133−33, 133, s)-Nets in Base 4

Best Known (133−33, 133, s)-Nets in Base 4

(133−33, 133, 1028)-Net over F₄ — Constructive and digital

Digital (100, 133, 1028)-net over F₄, using

4¹ times duplication [i] based on digital (99, 132, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 33, 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]

(133−33, 133, 1371)-Net over F₄ — Digital

Digital (100, 133, 1371)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−33, 133, 210080)-Net in Base 4 — Upper bound on s

There is no (100, 133, 210081)-net in base 4, because

1 times m-reduction [i] would yield (100, 132, 210081)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 29 643764 526668 569931 580221 160545 622505 778029 714153 302095 156212 189074 143468 844862 > 4¹³² [i]