MinT - Best Known (82, 82+62, s)-Nets in Base 2

Best Known (82, 82+62, s)-Nets in Base 2

(82, 82+62, 54)-Net over F₂ — Constructive and digital

Digital (82, 144, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 72, 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]

(82, 82+62, 60)-Net over F₂ — Digital

Digital (82, 144, 60)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+62, 267)-Net in Base 2 — Upper bound on s

There is no (82, 144, 268)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 23 226618 464379 916726 704931 820049 774728 424640 > 2¹⁴⁴ [i]