MinT - Best Known (82, 82+64, s)-Nets in Base 8

Best Known (82, 82+64, s)-Nets in Base 8

(82, 82+64, 354)-Net over F₈ — Constructive and digital

Digital (82, 146, 354)-net over F₈, using

4 times m-reduction [i] based on digital (82, 150, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 75, 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]

(82, 82+64, 418)-Net over F₈ — Digital

Digital (82, 146, 418)-net over F₈, using

trace code for nets [i] based on digital (9, 73, 209)-net over F₆₄, using
- net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
    - a curve from the manYPoints database [i]

(82, 82+64, 24086)-Net in Base 8 — Upper bound on s

There is no (82, 146, 24087)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 710534 432367 170661 928079 107529 778459 811923 751298 248015 338923 482680 306396 669197 544432 836738 556999 139957 131748 684097 502057 754168 907568 > 8¹⁴⁶ [i]