MinT - Best Known (64−28, 64, s)-Nets in Base 8

Best Known (64−28, 64, s)-Nets in Base 8

(64−28, 64, 208)-Net over F₈ — Constructive and digital

Digital (36, 64, 208)-net over F₈, using

2 times m-reduction [i] based on digital (36, 66, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 33, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(64−28, 64, 258)-Net over F₈ — Digital

Digital (36, 64, 258)-net over F₈, using

trace code for nets [i] based on digital (4, 32, 129)-net over F₆₄, using
- net from sequence [i] based on digital (4, 128)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 4 and N(F) ≥ 129, using
    - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

(64−28, 64, 11599)-Net in Base 8 — Upper bound on s

There is no (36, 64, 11600)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6278 106107 337264 622096 254729 739261 898513 820761 393508 196071 > 8⁶⁴ [i]