MinT - Best Known (70, 70+40, s)-Nets in Base 8

Best Known (70, 70+40, s)-Nets in Base 8

(70, 70+40, 354)-Net over F₈ — Constructive and digital

Digital (70, 110, 354)-net over F₈, using

16 times m-reduction [i] based on digital (70, 126, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 63, 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]

(70, 70+40, 516)-Net in Base 8 — Constructive

(70, 110, 516)-net in base 8, using

trace code for nets [i] based on (15, 55, 258)-net in base 64, using
- 1 times m-reduction [i] based on (15, 56, 258)-net in base 64, using
  - base change [i] based on digital (1, 42, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(70, 70+40, 795)-Net over F₈ — Digital

Digital (70, 110, 795)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+40, 109939)-Net in Base 8 — Upper bound on s

There is no (70, 110, 109940)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2187 394077 820295 334005 307825 169451 856836 876302 769816 750563 566102 660684 405188 756553 910626 971216 606024 > 8¹¹⁰ [i]