MinT - Best Known (82, 82+80, s)-Nets in Base 8

Best Known (82, 82+80, s)-Nets in Base 8

(82, 82+80, 160)-Net over F₈ — Constructive and digital

Digital (82, 162, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 81, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(82, 82+80, 225)-Net in Base 8 — Constructive

(82, 162, 225)-net in base 8, using

6 times m-reduction [i] based on (82, 168, 225)-net in base 8, using
- base change [i] based on digital (40, 126, 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]

(82, 82+80, 274)-Net over F₈ — Digital

Digital (82, 162, 274)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+80, 10212)-Net in Base 8 — Upper bound on s

There is no (82, 162, 10213)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 200 084304 860188 869301 206209 833540 383767 389260 171965 942291 404479 569158 049590 497442 538995 727676 389053 729826 534664 728902 158130 087832 851287 678004 934504 > 8¹⁶² [i]