MinT - Best Known (127−48, 127, s)-Nets in Base 4

Best Known (127−48, 127, s)-Nets in Base 4

(127−48, 127, 130)-Net over F₄ — Constructive and digital

Digital (79, 127, 130)-net over F₄, using

19 times m-reduction [i] based on digital (79, 146, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 73, 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]

(127−48, 127, 241)-Net over F₄ — Digital

Digital (79, 127, 241)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−48, 127, 4994)-Net in Base 4 — Upper bound on s

There is no (79, 127, 4995)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 29080 846454 947721 601763 004061 002620 587414 566848 056213 437764 171019 976592 035184 > 4¹²⁷ [i]