MinT - Best Known (133−35, 133, s)-Nets in Base 2

Best Known (133−35, 133, s)-Nets in Base 2

(133−35, 133, 135)-Net over F₂ — Constructive and digital

Digital (98, 133, 135)-net over F₂, using

2¹ times duplication [i] based on digital (97, 132, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 44, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(133−35, 133, 178)-Net over F₂ — Digital

Digital (98, 133, 178)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−35, 133, 1536)-Net in Base 2 — Upper bound on s

There is no (98, 133, 1537)-net in base 2, because

1 times m-reduction [i] would yield (98, 132, 1537)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5503 731489 951781 698044 989827 038026 901824 > 2¹³² [i]