MinT - Best Known (72, 72+52, s)-Nets in Base 2

Best Known (72, 72+52, s)-Nets in Base 2

(72, 72+52, 54)-Net over F₂ — Constructive and digital

Digital (72, 124, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 62, 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, 72+52, 56)-Net over F₂ — Digital

Digital (72, 124, 56)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+52, 251)-Net in Base 2 — Upper bound on s

There is no (72, 124, 252)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 22 433294 731666 803140 008025 602686 715501 > 2¹²⁴ [i]