MinT - Best Known (90, 142, s)-Nets in Base 8

Best Known (90, 142, s)-Nets in Base 8

(90, 142, 354)-Net over F₈ — Constructive and digital

Digital (90, 142, 354)-net over F₈, using

24 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]

(90, 142, 516)-Net in Base 8 — Constructive

(90, 142, 516)-net in base 8, using

trace code for nets [i] based on (19, 71, 258)-net in base 64, using
- 1 times m-reduction [i] based on (19, 72, 258)-net in base 64, using
  - base change [i] based on digital (1, 54, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(90, 142, 952)-Net over F₈ — Digital

Digital (90, 142, 952)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 142, 128943)-Net in Base 8 — Upper bound on s

There is no (90, 142, 128944)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 292336 415094 677564 423521 892945 792076 284247 297487 561963 157844 894359 471402 199176 949716 013670 859065 457094 359130 477052 320099 089318 > 8¹⁴² [i]