MinT - Best Known (64−28, 64, s)-Nets in Base 4

Best Known (64−28, 64, s)-Nets in Base 4

(64−28, 64, 90)-Net over F₄ — Constructive and digital

Digital (36, 64, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 32, 45)-net over F₁₆, using
- net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
    - a function field by GarcÃa and Quoos [i]

(64−28, 64, 1128)-Net in Base 4 — Upper bound on s

There is no (36, 64, 1129)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 344 048679 328602 047644 439953 326519 078544 > 4⁶⁴ [i]