MinT - Best Known (98, 98+39, s)-Nets in Base 2

Best Known (98, 98+39, s)-Nets in Base 2

(98, 98+39, 84)-Net over F₂ — Constructive and digital

Digital (98, 137, 84)-net over F₂, using

t-expansion [i] based on digital (97, 137, 84)-net over F₂, using
- 1 times m-reduction [i] based on digital (97, 138, 84)-net over F₂, using
  - trace code for nets [i] based on digital (5, 46, 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]

(98, 98+39, 148)-Net over F₂ — Digital

Digital (98, 137, 148)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+39, 1104)-Net in Base 2 — Upper bound on s

There is no (98, 137, 1105)-net in base 2, because

1 times m-reduction [i] would yield (98, 136, 1105)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 87702 132926 423667 349476 538027 372799 778728 > 2¹³⁶ [i]