MinT - Best Known (82, 82+52, s)-Nets in Base 2

Best Known (82, 82+52, s)-Nets in Base 2

(82, 82+52, 66)-Net over F₂ — Constructive and digital

Digital (82, 134, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 67, 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]

(82, 82+52, 71)-Net over F₂ — Digital

Digital (82, 134, 71)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+52, 338)-Net in Base 2 — Upper bound on s

There is no (82, 134, 339)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 22036 067703 097494 085915 148251 728482 427400 > 2¹³⁴ [i]