MinT - Best Known (102, 102+38, s)-Nets in Base 8

Best Known (102, 102+38, s)-Nets in Base 8

(102, 102+38, 1026)-Net over F₈ — Constructive and digital

Digital (102, 140, 1026)-net over F₈, using

8 times m-reduction [i] based on digital (102, 148, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 74, 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]

(102, 102+38, 5487)-Net over F₈ — Digital

Digital (102, 140, 5487)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+38, 5110504)-Net in Base 8 — Upper bound on s

There is no (102, 140, 5110505)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 707694 023207 390459 031938 623147 800060 112985 744417 417788 525765 849026 773862 532488 723230 783897 464938 911238 532056 785086 652844 155152 > 8¹⁴⁰ [i]