MinT - Best Known (84, 84+52, s)-Nets in Base 2

Best Known (84, 84+52, s)-Nets in Base 2

(84, 84+52, 66)-Net over F₂ — Constructive and digital

Digital (84, 136, 66)-net over F₂, using

2 times m-reduction [i] based on digital (84, 138, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 69, 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]

(84, 84+52, 75)-Net over F₂ — Digital

Digital (84, 136, 75)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+52, 359)-Net in Base 2 — Upper bound on s

There is no (84, 136, 360)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 91111 313731 635125 677912 761481 924655 838556 > 2¹³⁶ [i]