MinT - Best Known (75, 98, s)-Nets in Base 2

Best Known (75, 98, s)-Nets in Base 2

(75, 98, 135)-Net over F₂ — Constructive and digital

Digital (75, 98, 135)-net over F₂, using

1 times m-reduction [i] based on digital (75, 99, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 33, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(75, 98, 190)-Net over F₂ — Digital

Digital (75, 98, 190)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 98, 2199)-Net in Base 2 — Upper bound on s

There is no (75, 98, 2200)-net in base 2, because

1 times m-reduction [i] would yield (75, 97, 2200)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 158489 374349 653792 915857 051426 > 2⁹⁷ [i]