MinT - Best Known (64, 64+49, s)-Nets in Base 4

Best Known (64, 64+49, s)-Nets in Base 4

(64, 64+49, 130)-Net over F₄ — Constructive and digital

Digital (64, 113, 130)-net over F₄, using

3 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+49, 139)-Net over F₄ — Digital

Digital (64, 113, 139)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+49, 2088)-Net in Base 4 — Upper bound on s

There is no (64, 113, 2089)-net in base 4, because

1 times m-reduction [i] would yield (64, 112, 2089)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 27 116201 149647 306327 107721 616673 593063 538756 130534 917638 983327 493714 > 4¹¹² [i]