MinT - Best Known (167−51, 167, s)-Nets in Base 8

Best Known (167−51, 167, s)-Nets in Base 8

(167−51, 167, 1026)-Net over F₈ — Constructive and digital

Digital (116, 167, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 167, 1026)-net over F₈, using
- 5 times m-reduction [i] based on digital (114, 172, 1026)-net over F₈, using
  - trace code for nets [i] based on digital (28, 86, 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]

(167−51, 167, 2915)-Net over F₈ — Digital

Digital (116, 167, 2915)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−51, 167, 1442250)-Net in Base 8 — Upper bound on s

There is no (116, 167, 1442251)-net in base 8, because

1 times m-reduction [i] would yield (116, 166, 1442251)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 818358 809861 734201 438036 812187 206305 803195 594215 740002 184179 848628 492667 464490 749804 338975 446862 530486 149865 776937 219065 520792 760412 404855 768202 256648 > 8¹⁶⁶ [i]