MinT - Best Known (127−47, 127, s)-Nets in Base 4

Best Known (127−47, 127, s)-Nets in Base 4

(127−47, 127, 130)-Net over F₄ — Constructive and digital

Digital (80, 127, 130)-net over F₄, using

21 times m-reduction [i] based on digital (80, 148, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 74, 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]

(127−47, 127, 258)-Net over F₄ — Digital

Digital (80, 127, 258)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−47, 127, 6226)-Net in Base 4 — Upper bound on s

There is no (80, 127, 6227)-net in base 4, because

1 times m-reduction [i] would yield (80, 126, 6227)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7237 232158 630978 144888 596911 962543 681293 160512 347623 471327 966134 706282 457728 > 4¹²⁶ [i]