MinT - Best Known (49, 76, s)-Nets in Base 8

Best Known (49, 76, s)-Nets in Base 8

(49, 76, 354)-Net over F₈ — Constructive and digital

Digital (49, 76, 354)-net over F₈, using

8 times m-reduction [i] based on digital (49, 84, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 42, 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]

(49, 76, 516)-Net in Base 8 — Constructive

(49, 76, 516)-net in base 8, using

base change [i] based on digital (30, 57, 516)-net over F₁₆, using
- 1 times m-reduction [i] based on digital (30, 58, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 29, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(49, 76, 671)-Net over F₈ — Digital

Digital (49, 76, 671)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 76, 131345)-Net in Base 8 — Upper bound on s

There is no (49, 76, 131346)-net in base 8, because

1 times m-reduction [i] would yield (49, 75, 131346)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 53 920137 299250 124412 712704 808220 096626 717955 781604 572374 791468 385332 > 8⁷⁵ [i]