MinT - Best Known (71, 71+65, s)-Nets in Base 8

Best Known (71, 71+65, s)-Nets in Base 8

(71, 71+65, 208)-Net over F₈ — Constructive and digital

Digital (71, 136, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 68, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(71, 71+65, 271)-Net over F₈ — Digital

Digital (71, 136, 271)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+65, 11774)-Net in Base 8 — Upper bound on s

There is no (71, 136, 11775)-net in base 8, because

1 times m-reduction [i] would yield (71, 135, 11775)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 82 674504 808822 601193 686116 620407 368209 599381 168313 310214 644627 442273 342793 420530 605283 747949 286396 423891 270011 360425 377233 > 8¹³⁵ [i]