MinT - Best Known (62−26, 62, s)-Nets in Base 8

Best Known (62−26, 62, s)-Nets in Base 8

(62−26, 62, 256)-Net over F₈ — Constructive and digital

Digital (36, 62, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 31, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(62−26, 62, 258)-Net in Base 8 — Constructive

(36, 62, 258)-net in base 8, using

trace code for nets [i] based on (5, 31, 129)-net in base 64, using
- 4 times m-reduction [i] based on (5, 35, 129)-net in base 64, using
  - base change [i] based on digital (0, 30, 129)-net over F₁₂₈, using
    - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
        the rational function field F₁₂₈(x) [i]
      - Niederreiter sequence [i]

(62−26, 62, 266)-Net over F₈ — Digital

Digital (36, 62, 266)-net over F₈, using

trace code for nets [i] based on digital (5, 31, 133)-net over F₆₄, using
- net from sequence [i] based on digital (5, 132)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 133, using
    - a curve from the manYPoints database [i]

(62−26, 62, 16411)-Net in Base 8 — Upper bound on s

There is no (36, 62, 16412)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 98 128612 198504 210156 832637 578845 075273 157580 224473 644612 > 8⁶² [i]