MinT - Best Known (149−83, 149, s)-Nets in Base 8

Best Known (149−83, 149, s)-Nets in Base 8

(149−83, 149, 113)-Net over F₈ — Constructive and digital

Digital (66, 149, 113)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (11, 52, 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, 97, 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]

(149−83, 149, 157)-Net over F₈ — Digital

Digital (66, 149, 157)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−83, 149, 4169)-Net in Base 8 — Upper bound on s

There is no (66, 149, 4170)-net in base 8, because

1 times m-reduction [i] would yield (66, 148, 4170)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 712341 652721 277987 376895 087919 453109 502409 412146 887509 029694 063102 700352 308622 851018 378190 184502 308005 902422 239221 755004 718643 093170 > 8¹⁴⁸ [i]