MinT - Best Known (72−26, 72, s)-Nets in Base 2

Best Known (72−26, 72, s)-Nets in Base 2

(72−26, 72, 54)-Net over F₂ — Constructive and digital

Digital (46, 72, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 36, 27)-net over F₄, using
- net from sequence [i] based on digital (10, 26)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
    - an explicitly constructive algebraic function field [i]

(72−26, 72, 245)-Net in Base 2 — Upper bound on s

There is no (46, 72, 246)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4957 458536 414029 675738 > 2⁷² [i]