MinT - Best Known (93, 93+60, s)-Nets in Base 2

Best Known (93, 93+60, s)-Nets in Base 2

(93, 93+60, 66)-Net over F₂ — Constructive and digital

Digital (93, 153, 66)-net over F₂, using

3 times m-reduction [i] based on digital (93, 156, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 78, 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]

(93, 93+60, 77)-Net over F₂ — Digital

Digital (93, 153, 77)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 93+60, 370)-Net in Base 2 — Upper bound on s

There is no (93, 153, 371)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11709 069572 085539 642128 042529 023253 563071 045096 > 2¹⁵³ [i]