MinT - Best Known (167−67, 167, s)-Nets in Base 2

Best Known (167−67, 167, s)-Nets in Base 2

(167−67, 167, 66)-Net over F₂ — Constructive and digital

Digital (100, 167, 66)-net over F₂, using

3 times m-reduction [i] based on digital (100, 170, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 85, 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]

(167−67, 167, 79)-Net over F₂ — Digital

Digital (100, 167, 79)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−67, 167, 383)-Net in Base 2 — Upper bound on s

There is no (100, 167, 384)-net in base 2, because

1 times m-reduction [i] would yield (100, 166, 384)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 96 780890 852366 547411 149384 857521 881389 412289 087293 > 2¹⁶⁶ [i]