MinT - Best Known (126−55, 126, s)-Nets in Base 4

Best Known (126−55, 126, s)-Nets in Base 4

(126−55, 126, 130)-Net over F₄ — Constructive and digital

Digital (71, 126, 130)-net over F₄, using

4 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]

(126−55, 126, 149)-Net over F₄ — Digital

Digital (71, 126, 149)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−55, 126, 2209)-Net in Base 4 — Upper bound on s

There is no (71, 126, 2210)-net in base 4, because

1 times m-reduction [i] would yield (71, 125, 2210)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1818 016757 475860 679764 637980 006368 029926 381088 859932 503855 849254 544101 368208 > 4¹²⁵ [i]