MinT - Best Known (70, 70+35, s)-Nets in Base 4

Best Known (70, 70+35, s)-Nets in Base 4

(70, 70+35, 195)-Net over F₄ — Constructive and digital

Digital (70, 105, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 35, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(70, 70+35, 325)-Net over F₄ — Digital

Digital (70, 105, 325)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+35, 11521)-Net in Base 4 — Upper bound on s

There is no (70, 105, 11522)-net in base 4, because

1 times m-reduction [i] would yield (70, 104, 11522)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 411 826859 557167 142891 976184 264963 634477 471417 511059 548020 890960 > 4¹⁰⁴ [i]