MinT - Best Known (118−43, 118, s)-Nets in Base 8

Best Known (118−43, 118, s)-Nets in Base 8

(118−43, 118, 354)-Net over F₈ — Constructive and digital

Digital (75, 118, 354)-net over F₈, using

18 times m-reduction [i] based on digital (75, 136, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 68, 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]

(118−43, 118, 516)-Net in Base 8 — Constructive

(75, 118, 516)-net in base 8, using

trace code for nets [i] based on (16, 59, 258)-net in base 64, using
- 1 times m-reduction [i] based on (16, 60, 258)-net in base 64, using
  - base change [i] based on digital (1, 45, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(118−43, 118, 834)-Net over F₈ — Digital

Digital (75, 118, 834)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(118−43, 118, 133307)-Net in Base 8 — Upper bound on s

There is no (75, 118, 133308)-net in base 8, because

1 times m-reduction [i] would yield (75, 117, 133308)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4587 591236 097712 244861 490960 799390 015922 991353 279238 496408 593502 097256 179986 521689 157222 992362 501902 159154 > 8¹¹⁷ [i]