MinT - Best Known (144−65, 144, s)-Nets in Base 8

Best Known (144−65, 144, s)-Nets in Base 8

(144−65, 144, 354)-Net over F₈ — Constructive and digital

Digital (79, 144, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 72, 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]

(144−65, 144, 360)-Net over F₈ — Digital

Digital (79, 144, 360)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−65, 144, 19816)-Net in Base 8 — Upper bound on s

There is no (79, 144, 19817)-net in base 8, because

1 times m-reduction [i] would yield (79, 143, 19817)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1387 531967 626249 764048 308561 460199 118652 722818 731751 484979 019375 671280 771071 796434 324852 022876 510051 262261 894108 680674 465683 285883 > 8¹⁴³ [i]