MinT - Best Known (158−71, 158, s)-Nets in Base 8

Best Known (158−71, 158, s)-Nets in Base 8

(158−71, 158, 354)-Net over F₈ — Constructive and digital

Digital (87, 158, 354)-net over F₈, using

2 times m-reduction [i] based on digital (87, 160, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 80, 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]

(158−71, 158, 398)-Net over F₈ — Digital

Digital (87, 158, 398)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−71, 158, 22322)-Net in Base 8 — Upper bound on s

There is no (87, 158, 22323)-net in base 8, because

1 times m-reduction [i] would yield (87, 157, 22323)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6102 486241 384545 588877 752987 846747 191986 938432 762487 091224 681183 009715 264783 251371 313811 853353 140616 926795 170659 494303 548639 265872 709845 295512 > 8¹⁵⁷ [i]