MinT - Best Known (214−89, 214, s)-Nets in Base 2

Best Known (214−89, 214, s)-Nets in Base 2

(214−89, 214, 66)-Net over F₂ — Constructive and digital

Digital (125, 214, 66)-net over F₂, using

6 times m-reduction [i] based on digital (125, 220, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 110, 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]

(214−89, 214, 89)-Net over F₂ — Digital

Digital (125, 214, 89)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−89, 214, 432)-Net in Base 2 — Upper bound on s

There is no (125, 214, 433)-net in base 2, because

1 times m-reduction [i] would yield (125, 213, 433)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13498 912569 059590 836548 667448 186249 634369 346852 258042 682663 070820 > 2²¹³ [i]