MinT - Best Known (213−90, 213, s)-Nets in Base 2

Best Known (213−90, 213, s)-Nets in Base 2

(213−90, 213, 66)-Net over F₂ — Constructive and digital

Digital (123, 213, 66)-net over F₂, using

3 times m-reduction [i] based on digital (123, 216, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 108, 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]

(213−90, 213, 86)-Net over F₂ — Digital

Digital (123, 213, 86)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−90, 213, 405)-Net in Base 2 — Upper bound on s

There is no (123, 213, 406)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13253 163526 820550 684713 724388 438312 874843 842362 857043 591302 359544 > 2²¹³ [i]