MinT - Best Known (84, 84+54, s)-Nets in Base 8

Best Known (84, 84+54, s)-Nets in Base 8

(84, 84+54, 354)-Net over F₈ — Constructive and digital

Digital (84, 138, 354)-net over F₈, using

16 times m-reduction [i] based on digital (84, 154, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 77, 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]

(84, 84+54, 432)-Net in Base 8 — Constructive

(84, 138, 432)-net in base 8, using

trace code for nets [i] based on (15, 69, 216)-net in base 64, using
- 1 times m-reduction [i] based on (15, 70, 216)-net in base 64, using
  - base change [i] based on digital (5, 60, 216)-net over F₁₂₈, using
    - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(84, 84+54, 664)-Net over F₈ — Digital

Digital (84, 138, 664)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+54, 64415)-Net in Base 8 — Upper bound on s

There is no (84, 138, 64416)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42321 744699 120935 395365 295174 300687 386940 834231 299412 215618 593058 938602 039839 964766 602333 770486 790619 908476 865213 063684 632575 > 8¹³⁸ [i]