MinT - Best Known (164−74, 164, s)-Nets in Base 8

Best Known (164−74, 164, s)-Nets in Base 8

(164−74, 164, 354)-Net over F₈ — Constructive and digital

Digital (90, 164, 354)-net over F₈, using

2 times m-reduction [i] based on digital (90, 166, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 83, 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]

(164−74, 164, 404)-Net over F₈ — Digital

Digital (90, 164, 404)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−74, 164, 21048)-Net in Base 8 — Upper bound on s

There is no (90, 164, 21049)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12800 163597 648665 116229 537892 951283 187967 485513 927026 143741 788661 718128 539634 919562 277451 201927 896507 214098 396662 756564 990856 491482 974347 727551 212440 > 8¹⁶⁴ [i]