MinT - Best Known (72−24, 72, s)-Nets in Base 8

Best Known (72−24, 72, s)-Nets in Base 8

(72−24, 72, 354)-Net over F₈ — Constructive and digital

Digital (48, 72, 354)-net over F₈, using

10 times m-reduction [i] based on digital (48, 82, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 41, 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]

(72−24, 72, 520)-Net in Base 8 — Constructive

(48, 72, 520)-net in base 8, using

base change [i] based on digital (30, 54, 520)-net over F₁₆, using
- trace code for nets [i] based on digital (3, 27, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(72−24, 72, 916)-Net over F₈ — Digital

Digital (48, 72, 916)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(72−24, 72, 198055)-Net in Base 8 — Upper bound on s

There is no (48, 72, 198056)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 105313 825072 924091 231045 137591 699550 308738 938126 015359 162494 337484 > 8⁷² [i]