MinT - Best Known (163−61, 163, s)-Nets in Base 2

Best Known (163−61, 163, s)-Nets in Base 2

(163−61, 163, 66)-Net over F₂ — Constructive and digital

Digital (102, 163, 66)-net over F₂, using

11 times m-reduction [i] based on digital (102, 174, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 87, 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]

(163−61, 163, 91)-Net over F₂ — Digital

Digital (102, 163, 91)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−61, 163, 465)-Net in Base 2 — Upper bound on s

There is no (102, 163, 466)-net in base 2, because

1 times m-reduction [i] would yield (102, 162, 466)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 926956 480693 427242 957087 272949 690074 358673 216480 > 2¹⁶² [i]