MinT - Best Known (146−40, 146, s)-Nets in Base 8

Best Known (146−40, 146, s)-Nets in Base 8

(146−40, 146, 1026)-Net over F₈ — Constructive and digital

Digital (106, 146, 1026)-net over F₈, using

10 times m-reduction [i] based on digital (106, 156, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 78, 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]

(146−40, 146, 5305)-Net over F₈ — Digital

Digital (106, 146, 5305)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−40, 146, 4642628)-Net in Base 8 — Upper bound on s

There is no (106, 146, 4642629)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 709804 747650 937316 176237 879013 478345 424516 557535 608448 272688 056753 602950 499535 689561 079857 386881 105102 446404 224877 702805 913074 967196 > 8¹⁴⁶ [i]