MinT - Best Known (71, 98, s)-Nets in Base 2

Best Known (71, 98, s)-Nets in Base 2

(71, 98, 84)-Net over F₂ — Constructive and digital

Digital (71, 98, 84)-net over F₂, using

1 times m-reduction [i] based on digital (71, 99, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 33, 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]

(71, 98, 125)-Net over F₂ — Digital

Digital (71, 98, 125)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 98, 980)-Net in Base 2 — Upper bound on s

There is no (71, 98, 981)-net in base 2, because

1 times m-reduction [i] would yield (71, 97, 981)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 160253 941102 724255 228578 507604 > 2⁹⁷ [i]