MinT - Best Known (88, 88+64, s)-Nets in Base 8

Best Known (88, 88+64, s)-Nets in Base 8

(88, 88+64, 354)-Net over F₈ — Constructive and digital

Digital (88, 152, 354)-net over F₈, using

10 times m-reduction [i] based on digital (88, 162, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 81, 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, 88+64, 514)-Net over F₈ — Digital

Digital (88, 152, 514)-net over F₈, using

trace code for nets [i] based on digital (12, 76, 257)-net over F₆₄, using
- net from sequence [i] based on digital (12, 256)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 12 and N(F) ≥ 257, using
    - K_1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

(88, 88+64, 35580)-Net in Base 8 — Upper bound on s

There is no (88, 152, 35581)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186115 424989 755799 127649 412164 874667 460201 318232 520369 284798 549617 237020 852137 675969 100506 242045 541977 406781 872911 889392 976350 844464 903945 > 8¹⁵² [i]