MinT - Best Known (144−54, 144, s)-Nets in Base 8

Best Known (144−54, 144, s)-Nets in Base 8

(144−54, 144, 354)-Net over F₈ — Constructive and digital

Digital (90, 144, 354)-net over F₈, using

22 times m-reduction [i] based on digital (90, 166, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 83, 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]

(144−54, 144, 514)-Net in Base 8 — Constructive

(90, 144, 514)-net in base 8, using

base change [i] based on digital (54, 108, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 54, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(144−54, 144, 851)-Net over F₈ — Digital

Digital (90, 144, 851)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−54, 144, 102262)-Net in Base 8 — Upper bound on s

There is no (90, 144, 102263)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11091 677556 143484 168670 399886 452226 070545 002726 111612 835528 819960 412754 786219 273194 080864 251251 870278 257238 446613 733467 265837 022416 > 8¹⁴⁴ [i]