MinT - Best Known (170−67, 170, s)-Nets in Base 2

Best Known (170−67, 170, s)-Nets in Base 2

(170−67, 170, 66)-Net over F₂ — Constructive and digital

Digital (103, 170, 66)-net over F₂, using

6 times m-reduction [i] based on digital (103, 176, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 88, 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]

(170−67, 170, 83)-Net over F₂ — Digital

Digital (103, 170, 83)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−67, 170, 411)-Net in Base 2 — Upper bound on s

There is no (103, 170, 412)-net in base 2, because

1 times m-reduction [i] would yield (103, 169, 412)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 781 641926 242960 333183 729633 235191 800877 596858 873500 > 2¹⁶⁹ [i]