MinT - Best Known (58, 58+28, s)-Nets in Base 2

Best Known (58, 58+28, s)-Nets in Base 2

(58, 58+28, 66)-Net over F₂ — Constructive and digital

Digital (58, 86, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 43, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(58, 58+28, 76)-Net over F₂ — Digital

Digital (58, 86, 76)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+28, 407)-Net in Base 2 — Upper bound on s

There is no (58, 86, 408)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 79 571946 804764 446171 011382 > 2⁸⁶ [i]