MinT - Best Known (171, 228, s)-Nets in Base 4

Best Known (171, 228, s)-Nets in Base 4

(171, 228, 1028)-Net over F₄ — Constructive and digital

Digital (171, 228, 1028)-net over F₄, using

trace code for nets [i] based on digital (0, 57, 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]

(171, 228, 2073)-Net over F₄ — Digital

Digital (171, 228, 2073)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 228, 286309)-Net in Base 4 — Upper bound on s

There is no (171, 228, 286310)-net in base 4, because

1 times m-reduction [i] would yield (171, 227, 286310)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46520 727830 202936 840009 162328 211631 333492 128645 109727 456498 248446 856885 308090 487377 098683 158385 730096 754849 924937 188845 415058 072040 021180 > 4²²⁷ [i]