MinT - Best Known (68, 68+50, s)-Nets in Base 2

Best Known (68, 68+50, s)-Nets in Base 2

(68, 68+50, 44)-Net over F₂ — Constructive and digital

Digital (68, 118, 44)-net over F₂, using

trace code for nets [i] based on digital (9, 59, 22)-net over F₄, using
- net from sequence [i] based on digital (9, 21)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 22, using
    - an explicitly constructive algebraic function field [i]

(68, 68+50, 53)-Net over F₂ — Digital

Digital (68, 118, 53)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+50, 233)-Net in Base 2 — Upper bound on s

There is no (68, 118, 234)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 352127 806315 714718 898984 163438 931066 > 2¹¹⁸ [i]