MinT - Best Known (82, 113, s)-Nets in Base 2

Best Known (82, 113, s)-Nets in Base 2

(82, 113, 84)-Net over F₂ — Constructive and digital

Digital (82, 113, 84)-net over F₂, using

t-expansion [i] based on digital (81, 113, 84)-net over F₂, using
- 1 times m-reduction [i] based on digital (81, 114, 84)-net over F₂, using
  - trace code for nets [i] based on digital (5, 38, 28)-net over F₈, using
    - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
        a function field by SÃ©mirat [i]

(82, 113, 141)-Net over F₂ — Digital

Digital (82, 113, 141)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 113, 1114)-Net in Base 2 — Upper bound on s

There is no (82, 113, 1115)-net in base 2, because

1 times m-reduction [i] would yield (82, 112, 1115)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5233 759041 562881 346652 060366 975048 > 2¹¹² [i]