MinT - Best Known (64, 64+45, s)-Nets in Base 4

Best Known (64, 64+45, s)-Nets in Base 4

(64, 64+45, 130)-Net over F₄ — Constructive and digital

Digital (64, 109, 130)-net over F₄, using

7 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+45, 158)-Net over F₄ — Digital

Digital (64, 109, 158)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+45, 2706)-Net in Base 4 — Upper bound on s

There is no (64, 109, 2707)-net in base 4, because

1 times m-reduction [i] would yield (64, 108, 2707)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 105492 670078 237934 133466 412050 223382 452963 841231 789293 663561 927200 > 4¹⁰⁸ [i]