MinT - Best Known (71, 128, s)-Nets in Base 4

Best Known (71, 128, s)-Nets in Base 4

(71, 128, 130)-Net over F₄ — Constructive and digital

Digital (71, 128, 130)-net over F₄, using

2 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, 128, 142)-Net over F₄ — Digital

Digital (71, 128, 142)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 128, 2003)-Net in Base 4 — Upper bound on s

There is no (71, 128, 2004)-net in base 4, because

1 times m-reduction [i] would yield (71, 127, 2004)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 29212 516508 655795 474353 678846 713688 623954 569850 405572 052903 120905 081741 117808 > 4¹²⁷ [i]