MinT - Best Known (143−79, 143, s)-Nets in Base 8

Best Known (143−79, 143, s)-Nets in Base 8

(143−79, 143, 113)-Net over F₈ — Constructive and digital

Digital (64, 143, 113)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (11, 50, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]
2. digital (14, 93, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(143−79, 143, 157)-Net over F₈ — Digital

Digital (64, 143, 157)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−79, 143, 4246)-Net in Base 8 — Upper bound on s

There is no (64, 143, 4247)-net in base 8, because

1 times m-reduction [i] would yield (64, 142, 4247)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 174 577009 489989 060964 544855 687465 194584 269777 456191 799585 119995 433230 835922 203624 300637 993542 318956 597321 553046 954545 106469 431712 > 8¹⁴² [i]