MinT - Best Known (64, 64+51, s)-Nets in Base 4

Best Known (64, 64+51, s)-Nets in Base 4

(64, 64+51, 130)-Net over F₄ — Constructive and digital

Digital (64, 115, 130)-net over F₄, using

1 times m-reduction [i] based on digital (64, 116, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 58, 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]

(64, 64+51, 131)-Net over F₄ — Digital

Digital (64, 115, 131)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+51, 1867)-Net in Base 4 — Upper bound on s

There is no (64, 115, 1868)-net in base 4, because

1 times m-reduction [i] would yield (64, 114, 1868)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 435 381244 891236 685196 264166 752882 894672 642087 385664 122134 006192 914036 > 4¹¹⁴ [i]