MinT - Best Known (84, 84+67, s)-Nets in Base 4

Best Known (84, 84+67, s)-Nets in Base 4

(84, 84+67, 130)-Net over F₄ — Constructive and digital

Digital (84, 151, 130)-net over F₄, using

5 times m-reduction [i] based on digital (84, 156, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 78, 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]

(84, 84+67, 165)-Net over F₄ — Digital

Digital (84, 151, 165)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+67, 2365)-Net in Base 4 — Upper bound on s

There is no (84, 151, 2366)-net in base 4, because

1 times m-reduction [i] would yield (84, 150, 2366)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 045164 012944 955074 641542 292207 360176 608342 158724 846679 285557 127565 033395 182394 012276 920697 > 4¹⁵⁰ [i]