MinT - Best Known (96, 96+61, s)-Nets in Base 2

Best Known (96, 96+61, s)-Nets in Base 2

(96, 96+61, 66)-Net over F₂ — Constructive and digital

Digital (96, 157, 66)-net over F₂, using

5 times m-reduction [i] based on digital (96, 162, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 81, 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]

(96, 96+61, 81)-Net over F₂ — Digital

Digital (96, 157, 81)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 96+61, 400)-Net in Base 2 — Upper bound on s

There is no (96, 157, 401)-net in base 2, because

1 times m-reduction [i] would yield (96, 156, 401)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 96629 878305 799600 251055 118284 016461 534202 360256 > 2¹⁵⁶ [i]