MinT - Best Known (118, 118+50, s)-Nets in Base 8

Best Known (118, 118+50, s)-Nets in Base 8

(118, 118+50, 1026)-Net over F₈ — Constructive and digital

Digital (118, 168, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 168, 1026)-net over F₈, using
- 4 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]

(118, 118+50, 3433)-Net over F₈ — Digital

Digital (118, 168, 3433)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 118+50, 1703289)-Net in Base 8 — Upper bound on s

There is no (118, 168, 1703290)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 52 374452 449750 553669 224439 708779 724806 823794 457579 278967 868697 630618 756683 062175 668310 684149 003210 965380 722956 287470 551839 991793 310542 003963 704317 689425 > 8¹⁶⁸ [i]