MinT - Best Known (164−52, 164, s)-Nets in Base 8

Best Known (164−52, 164, s)-Nets in Base 8

(164−52, 164, 1026)-Net over F₈ — Constructive and digital

Digital (112, 164, 1026)-net over F₈, using

4 times m-reduction [i] based on digital (112, 168, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 84, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(164−52, 164, 2300)-Net over F₈ — Digital

Digital (112, 164, 2300)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−52, 164, 749202)-Net in Base 8 — Upper bound on s

There is no (112, 164, 749203)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12786 791535 541898 244160 812108 400240 348021 819192 775485 097808 891228 075150 331676 751016 223897 581421 811264 397408 798759 793543 993515 492826 654231 153420 199568 > 8¹⁶⁴ [i]