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

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

(71, 71+71, 130)-Net over F₈ — Constructive and digital

Digital (71, 142, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 71, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(71, 71+71, 233)-Net over F₈ — Digital

Digital (71, 142, 233)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+71, 8614)-Net in Base 8 — Upper bound on s

There is no (71, 142, 8615)-net in base 8, because

1 times m-reduction [i] would yield (71, 141, 8615)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 21 720548 304451 280446 182379 253831 863675 307251 987848 116017 446203 868887 824135 372977 524502 960403 878725 305861 456488 998827 085426 717412 > 8¹⁴¹ [i]