MinT - Best Known (101, 101+85, s)-Nets in Base 4

Best Known (101, 101+85, s)-Nets in Base 4

(101, 101+85, 130)-Net over F₄ — Constructive and digital

Digital (101, 186, 130)-net over F₄, using

4 times m-reduction [i] based on digital (101, 190, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 95, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(101, 101+85, 179)-Net over F₄ — Digital

Digital (101, 186, 179)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+85, 2435)-Net in Base 4 — Upper bound on s

There is no (101, 186, 2436)-net in base 4, because

1 times m-reduction [i] would yield (101, 185, 2436)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2437 953217 196546 342257 911808 722204 129056 128837 933122 207804 946785 747062 661722 288974 017397 062009 438185 669587 919920 > 4¹⁸⁵ [i]