MinT - Best Known (56, 56+32, s)-Nets in Base 8

Best Known (56, 56+32, s)-Nets in Base 8

(56, 56+32, 354)-Net over F₈ — Constructive and digital

Digital (56, 88, 354)-net over F₈, using

10 times m-reduction [i] based on digital (56, 98, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 49, 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]

(56, 56+32, 516)-Net in Base 8 — Constructive

(56, 88, 516)-net in base 8, using

base change [i] based on digital (34, 66, 516)-net over F₁₆, using
- trace code for nets [i] based on digital (1, 33, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(56, 56+32, 665)-Net over F₈ — Digital

Digital (56, 88, 665)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+32, 90030)-Net in Base 8 — Upper bound on s

There is no (56, 88, 90031)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 29 646773 674458 800281 858357 456944 557284 249028 540450 860896 986961 175068 819546 863778 > 8⁸⁸ [i]