MinT - Best Known (88−30, 88, s)-Nets in Base 8

Best Known (88−30, 88, s)-Nets in Base 8

(88−30, 88, 354)-Net over F₈ — Constructive and digital

Digital (58, 88, 354)-net over F₈, using

14 times m-reduction [i] based on digital (58, 102, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 51, 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]

(88−30, 88, 520)-Net in Base 8 — Constructive

(58, 88, 520)-net in base 8, using

base change [i] based on digital (36, 66, 520)-net over F₁₆, using
- trace code for nets [i] based on digital (3, 33, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(88−30, 88, 932)-Net over F₈ — Digital

Digital (58, 88, 932)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−30, 88, 182294)-Net in Base 8 — Upper bound on s

There is no (58, 88, 182295)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 29 642788 501712 430862 452615 841040 261917 610417 345440 513791 283253 519827 755502 032000 > 8⁸⁸ [i]