MinT - Best Known (167−53, 167, s)-Nets in Base 8

Best Known (167−53, 167, s)-Nets in Base 8

(167−53, 167, 1026)-Net over F₈ — Constructive and digital

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]

(167−53, 167, 2323)-Net over F₈ — Digital

Digital (114, 167, 2323)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−53, 167, 879162)-Net in Base 8 — Upper bound on s

There is no (114, 167, 879163)-net in base 8, because

1 times m-reduction [i] would yield (114, 166, 879163)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 818356 848017 616822 263118 063898 954243 728731 467364 757091 977808 916774 044728 007609 274502 572682 926887 804417 880938 123919 824428 475826 082599 742933 557681 593115 > 8¹⁶⁶ [i]