MinT - Best Known (65, 65+33, s)-Nets in Base 2

Best Known (65, 65+33, s)-Nets in Base 2

(65, 65+33, 66)-Net over F₂ — Constructive and digital

Digital (65, 98, 66)-net over F₂, using

2 times m-reduction [i] based on digital (65, 100, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 50, 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]

(65, 65+33, 78)-Net over F₂ — Digital

Digital (65, 98, 78)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+33, 431)-Net in Base 2 — Upper bound on s

There is no (65, 98, 432)-net in base 2, because

1 times m-reduction [i] would yield (65, 97, 432)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 161072 864201 130962 129678 645410 > 2⁹⁷ [i]