MinT - Best Known (49, 49+47, s)-Nets in Base 8

Best Known (49, 49+47, s)-Nets in Base 8

(49, 49+47, 160)-Net over F₈ — Constructive and digital

Digital (49, 96, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 48, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(49, 49+47, 185)-Net over F₈ — Digital

Digital (49, 96, 185)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 49+47, 7221)-Net in Base 8 — Upper bound on s

There is no (49, 96, 7222)-net in base 8, because

1 times m-reduction [i] would yield (49, 95, 7222)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 62 174122 412784 481614 765515 938030 345083 985929 443826 166965 026150 040681 974488 770560 060016 > 8⁹⁵ [i]