MinT - Best Known (173−86, 173, s)-Nets in Base 8

Best Known (173−86, 173, s)-Nets in Base 8

(173−86, 173, 194)-Net over F₈ — Constructive and digital

Digital (87, 173, 194)-net over F₈, using

t-expansion [i] based on digital (85, 173, 194)-net over F₈, using
- net from sequence [i] based on digital (85, 193)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 85 and N(F) ≥ 194, using
    - F₆ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(173−86, 173, 225)-Net in Base 8 — Constructive

(87, 173, 225)-net in base 8, using

8¹ times duplication [i] based on (86, 172, 225)-net in base 8, using
- t-expansion [i] based on (83, 172, 225)-net in base 8, using
  - base change [i] based on digital (40, 129, 225)-net over F₁₆, using
    - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
        a function field by GarcÃa and Quoos [i]

(173−86, 173, 282)-Net over F₈ — Digital

Digital (87, 173, 282)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−86, 173, 10341)-Net in Base 8 — Upper bound on s

There is no (87, 173, 10342)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 717801 590008 238281 294364 106903 690604 785322 058652 604856 200058 483591 461114 791379 251800 175938 452607 707724 680985 484700 815426 005878 997159 045940 938839 792524 198000 > 8¹⁷³ [i]