MinT - Best Known (82, 82+24, s)-Nets in Base 2

Best Known (82, 82+24, s)-Nets in Base 2

(82, 82+24, 144)-Net over F₂ — Constructive and digital

Digital (82, 106, 144)-net over F₂, using

2¹ times duplication [i] based on digital (81, 105, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 35, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(82, 82+24, 222)-Net over F₂ — Digital

Digital (82, 106, 222)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+24, 2395)-Net in Base 2 — Upper bound on s

There is no (82, 106, 2396)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 81 528176 002480 586336 068918 992164 > 2¹⁰⁶ [i]