MinT - Best Known (147−63, 147, s)-Nets in Base 4

Best Known (147−63, 147, s)-Nets in Base 4

(147−63, 147, 130)-Net over F₄ — Constructive and digital

Digital (84, 147, 130)-net over F₄, using

9 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]

(147−63, 147, 179)-Net over F₄ — Digital

Digital (84, 147, 179)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−63, 147, 2808)-Net in Base 4 — Upper bound on s

There is no (84, 147, 2809)-net in base 4, because

1 times m-reduction [i] would yield (84, 146, 2809)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7967 174534 786918 400616 923982 540171 609179 990285 755577 247806 145457 979247 189239 515391 817120 > 4¹⁴⁶ [i]