MinT - Best Known (64−30, 64, s)-Nets in Base 4

Best Known (64−30, 64, s)-Nets in Base 4

(64−30, 64, 66)-Net over F₄ — Constructive and digital

Digital (34, 64, 66)-net over F₄, using

trace code for nets [i] based on digital (2, 32, 33)-net over F₁₆, using
- net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]

(64−30, 64, 70)-Net over F₄ — Digital

Digital (34, 64, 70)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(64−30, 64, 781)-Net in Base 4 — Upper bound on s

There is no (34, 64, 782)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 344 391433 768602 684127 980632 758120 204528 > 4⁶⁴ [i]