MinT - Best Known (62, 62+32, s)-Nets in Base 8

Best Known (62, 62+32, s)-Nets in Base 8

(62, 62+32, 363)-Net over F₈ — Constructive and digital

Digital (62, 94, 363)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (0, 16, 9)-net over F₈, using
  - net from sequence [i] based on digital (0, 8)-sequence over F₈, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 0 and N(F) ≥ 9, using
      - the rational function field F₈(x) [i]
    - Niederreiter sequence [i]
2. digital (46, 78, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 39, 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+32, 520)-Net in Base 8 — Constructive

(62, 94, 520)-net in base 8, using

trace code for nets [i] based on (15, 47, 260)-net in base 64, using
- 1 times m-reduction [i] based on (15, 48, 260)-net in base 64, using
  - base change [i] based on digital (3, 36, 260)-net over F₂₅₆, using
    - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(62, 62+32, 987)-Net over F₈ — Digital

Digital (62, 94, 987)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+32, 196368)-Net in Base 8 — Upper bound on s

There is no (62, 94, 196369)-net in base 8, because

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]