MinT - Best Known (123−33, 123, s)-Nets in Base 8

Best Known (123−33, 123, s)-Nets in Base 8

(123−33, 123, 1026)-Net over F₈ — Constructive and digital

Digital (90, 123, 1026)-net over F₈, using

1 times m-reduction [i] based on digital (90, 124, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 62, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(123−33, 123, 5424)-Net over F₈ — Digital

Digital (90, 123, 5424)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−33, 123, 7473108)-Net in Base 8 — Upper bound on s

There is no (90, 123, 7473109)-net in base 8, because

1 times m-reduction [i] would yield (90, 122, 7473109)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 150 307002 392349 519701 264830 335577 777009 568782 679538 754330 985880 694008 737187 267300 072618 320356 353508 589122 910449 > 8¹²² [i]