MinT - Best Known (59, 59+33, s)-Nets in Base 8

Best Known (59, 59+33, s)-Nets in Base 8

(59, 59+33, 354)-Net over F₈ — Constructive and digital

Digital (59, 92, 354)-net over F₈, using

12 times m-reduction [i] based on digital (59, 104, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 52, 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]

(59, 59+33, 516)-Net in Base 8 — Constructive

(59, 92, 516)-net in base 8, using

base change [i] based on digital (36, 69, 516)-net over F₁₆, using
- 1 times m-reduction [i] based on digital (36, 70, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 35, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(59, 59+33, 737)-Net over F₈ — Digital

Digital (59, 92, 737)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+33, 132963)-Net in Base 8 — Upper bound on s

There is no (59, 92, 132964)-net in base 8, because

1 times m-reduction [i] would yield (59, 91, 132964)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 15177 686032 905333 238523 544991 224540 030428 274956 723064 625024 594118 476759 922457 743394 > 8⁹¹ [i]