MinT - Best Known (62, 62+33, s)-Nets in Base 8

Best Known (62, 62+33, s)-Nets in Base 8

(62, 62+33, 354)-Net over F₈ — Constructive and digital

Digital (62, 95, 354)-net over F₈, using

15 times m-reduction [i] based on digital (62, 110, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 55, 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]

(62, 62+33, 518)-Net in Base 8 — Constructive

(62, 95, 518)-net in base 8, using

1 times m-reduction [i] based on (62, 96, 518)-net in base 8, using
- base change [i] based on digital (38, 72, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 36, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(62, 62+33, 893)-Net over F₈ — Digital

Digital (62, 95, 893)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+33, 196368)-Net in Base 8 — Upper bound on s

There is no (62, 95, 196369)-net in base 8, because

1 times m-reduction [i] would yield (62, 94, 196369)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 7 770736 196537 350190 564564 182866 432718 563762 201451 818428 613035 647600 262237 968983 133265 > 8⁹⁴ [i]