MinT - Best Known (99, 99+42, s)-Nets in Base 2

Best Known (99, 99+42, s)-Nets in Base 2

(99, 99+42, 84)-Net over F₂ — Constructive and digital

Digital (99, 141, 84)-net over F₂, using

trace code for nets [i] based on digital (5, 47, 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]

(99, 99+42, 136)-Net over F₂ — Digital

Digital (99, 141, 136)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+42, 880)-Net in Base 2 — Upper bound on s

There is no (99, 141, 881)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 797889 618064 895522 795283 960773 147035 059696 > 2¹⁴¹ [i]