MinT - Best Known (71, 71+69, s)-Nets in Base 8

Best Known (71, 71+69, s)-Nets in Base 8

(71, 71+69, 160)-Net over F₈ — Constructive and digital

Digital (71, 140, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 70, 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]

(71, 71+69, 244)-Net over F₈ — Digital

Digital (71, 140, 244)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+69, 9493)-Net in Base 8 — Upper bound on s

There is no (71, 140, 9494)-net in base 8, because

1 times m-reduction [i] would yield (71, 139, 9494)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 338531 565181 285414 989499 420437 113325 947418 122777 995645 013757 390196 572958 118732 799153 857394 264786 446821 481578 918944 459286 077072 > 8¹³⁹ [i]