MinT - Best Known (36, 36+17, s)-Nets in Base 8

Best Known (36, 36+17, s)-Nets in Base 8

(36, 36+17, 354)-Net over F₈ — Constructive and digital

Digital (36, 53, 354)-net over F₈, using

5 times m-reduction [i] based on digital (36, 58, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 29, 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]

(36, 36+17, 518)-Net in Base 8 — Constructive

(36, 53, 518)-net in base 8, using

1 times m-reduction [i] based on (36, 54, 518)-net in base 8, using
- trace code for nets [i] based on (9, 27, 259)-net in base 64, using
  - 1 times m-reduction [i] based on (9, 28, 259)-net in base 64, using
    - base change [i] based on digital (2, 21, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(36, 36+17, 961)-Net over F₈ — Digital

Digital (36, 53, 961)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(36, 36+17, 398723)-Net in Base 8 — Upper bound on s

There is no (36, 53, 398724)-net in base 8, because

1 times m-reduction [i] would yield (36, 52, 398724)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 91344 682953 556610 306256 022430 049772 879338 181520 > 8⁵² [i]