MinT - Best Known (218−94, 218, s)-Nets in Base 2

Best Known (218−94, 218, s)-Nets in Base 2

(218−94, 218, 66)-Net over F₂ — Constructive and digital

Digital (124, 218, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 109, 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]

(218−94, 218, 84)-Net over F₂ — Digital

Digital (124, 218, 84)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−94, 218, 391)-Net in Base 2 — Upper bound on s

There is no (124, 218, 392)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 421350 316910 179475 173433 016955 375185 994890 554659 163582 684187 480592 > 2²¹⁸ [i]