MinT - Best Known (84, 84+77, s)-Nets in Base 8

Best Known (84, 84+77, s)-Nets in Base 8

(84, 84+77, 208)-Net over F₈ — Constructive and digital

Digital (84, 161, 208)-net over F₈, using

1 times m-reduction [i] based on digital (84, 162, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 81, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(84, 84+77, 225)-Net in Base 8 — Constructive

(84, 161, 225)-net in base 8, using

t-expansion [i] based on (83, 161, 225)-net in base 8, using
- 11 times m-reduction [i] based on (83, 172, 225)-net in base 8, using
  - base change [i] based on digital (40, 129, 225)-net over F₁₆, using
    - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
        a function field by GarcÃa and Quoos [i]

(84, 84+77, 311)-Net over F₈ — Digital

Digital (84, 161, 311)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+77, 13596)-Net in Base 8 — Upper bound on s

There is no (84, 161, 13597)-net in base 8, because

1 times m-reduction [i] would yield (84, 160, 13597)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 126401 086480 163497 747260 036566 097737 134313 566251 119196 617266 502841 891196 742455 142368 933150 068677 150622 160675 362307 812566 226118 156201 545739 290144 > 8¹⁶⁰ [i]