MinT - Best Known (122−51, 122, s)-Nets in Base 8

Best Known (122−51, 122, s)-Nets in Base 8

(122−51, 122, 354)-Net over F₈ — Constructive and digital

Digital (71, 122, 354)-net over F₈, using

6 times m-reduction [i] based on digital (71, 128, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 64, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(122−51, 122, 450)-Net over F₈ — Digital

Digital (71, 122, 450)-net over F₈, using

trace code for nets [i] based on digital (10, 61, 225)-net over F₆₄, using
- net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(122−51, 122, 34141)-Net in Base 8 — Upper bound on s

There is no (71, 122, 34142)-net in base 8, because

1 times m-reduction [i] would yield (71, 121, 34142)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 18 792270 427886 762857 002690 918546 239029 062058 206183 334316 942558 135392 771394 213433 414307 978091 238357 928073 921613 > 8¹²¹ [i]