MinT - Best Known (71, 112, s)-Nets in Base 4

Best Known (71, 112, s)-Nets in Base 4

(71, 112, 130)-Net over F₄ — Constructive and digital

Digital (71, 112, 130)-net over F₄, using

18 times m-reduction [i] based on digital (71, 130, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 65, 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]

(71, 112, 242)-Net over F₄ — Digital

Digital (71, 112, 242)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 112, 6059)-Net in Base 4 — Upper bound on s

There is no (71, 112, 6060)-net in base 4, because

1 times m-reduction [i] would yield (71, 111, 6060)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 743265 967044 164560 844807 798185 663049 716195 083559 058271 803225 163004 > 4¹¹¹ [i]