MinT - Best Known (243−107, 243, s)-Nets in Base 2

Best Known (243−107, 243, s)-Nets in Base 2

(243−107, 243, 66)-Net over F₂ — Constructive and digital

Digital (136, 243, 66)-net over F₂, using

9 times m-reduction [i] based on digital (136, 252, 66)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 97, 33)-net over F₂, using
    - net from sequence [i] based on digital (39, 32)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
        an explicitly constructive algebraic function field [i]
  2. digital (39, 155, 33)-net over F₂, using
    - net from sequence [i] based on digital (39, 32)-sequence over F₂ (see above)

(243−107, 243, 87)-Net over F₂ — Digital

Digital (136, 243, 87)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−107, 243, 414)-Net in Base 2 — Upper bound on s

There is no (136, 243, 415)-net in base 2, because

1 times m-reduction [i] would yield (136, 242, 415)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 671200 618360 586279 916574 895371 529159 125840 727297 516190 922781 186758 893168 > 2²⁴² [i]