MinT - Best Known (161−63, 161, s)-Nets in Base 2

Best Known (161−63, 161, s)-Nets in Base 2

(161−63, 161, 66)-Net over F₂ — Constructive and digital

Digital (98, 161, 66)-net over F₂, using

5 times m-reduction [i] based on digital (98, 166, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 83, 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]

(161−63, 161, 81)-Net over F₂ — Digital

Digital (98, 161, 81)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(161−63, 161, 400)-Net in Base 2 — Upper bound on s

There is no (98, 161, 401)-net in base 2, because

1 times m-reduction [i] would yield (98, 160, 401)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 522053 376620 608343 938945 427157 229968 362585 280512 > 2¹⁶⁰ [i]