MinT - Best Known (61, 61+53, s)-Nets in Base 8

Best Known (61, 61+53, s)-Nets in Base 8

(61, 61+53, 208)-Net over F₈ — Constructive and digital

Digital (61, 114, 208)-net over F₈, using

2 times m-reduction [i] based on digital (61, 116, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 58, 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]

(61, 61+53, 262)-Net over F₈ — Digital

Digital (61, 114, 262)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+53, 12665)-Net in Base 8 — Upper bound on s

There is no (61, 114, 12666)-net in base 8, because

1 times m-reduction [i] would yield (61, 113, 12666)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 122009 615322 405161 494318 546244 331539 456663 723167 223351 722717 074237 051136 153081 239795 556892 453360 837280 > 8¹¹³ [i]