MinT - Best Known (61, 61+32, s)-Nets in Base 8

Best Known (61, 61+32, s)-Nets in Base 8

(61, 61+32, 354)-Net over F₈ — Constructive and digital

Digital (61, 93, 354)-net over F₈, using

15 times m-reduction [i] based on digital (61, 108, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 54, 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]

(61, 61+32, 518)-Net in Base 8 — Constructive

(61, 93, 518)-net in base 8, using

1 times m-reduction [i] based on (61, 94, 518)-net in base 8, using
- trace code for nets [i] based on (14, 47, 259)-net in base 64, using
  - 1 times m-reduction [i] based on (14, 48, 259)-net in base 64, using
    - base change [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]

(61, 61+32, 924)-Net over F₈ — Digital

Digital (61, 93, 924)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+32, 172435)-Net in Base 8 — Upper bound on s

There is no (61, 93, 172436)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 971382 792360 988251 828575 937503 629604 628408 017513 334745 019503 719704 870697 029338 630353 > 8⁹³ [i]