MinT - Best Known (214−53, 214, s)-Nets in Base 4

Best Known (214−53, 214, s)-Nets in Base 4

(214−53, 214, 1028)-Net over F₄ — Constructive and digital

Digital (161, 214, 1028)-net over F₄, using

4² times duplication [i] based on 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]

(214−53, 214, 2051)-Net over F₄ — Digital

Digital (161, 214, 2051)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−53, 214, 300885)-Net in Base 4 — Upper bound on s

There is no (161, 214, 300886)-net in base 4, because

1 times m-reduction [i] would yield (161, 213, 300886)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 173 292349 822047 382530 647478 253628 710930 350204 897699 555928 247490 889156 343368 277108 665449 760299 249784 470139 438250 504584 847604 300496 > 4²¹³ [i]