MinT - Best Known (30, 30+33, s)-Nets in Base 8

Best Known (30, 30+33, s)-Nets in Base 8

(30, 30+33, 74)-Net over F₈ — Constructive and digital

Digital (30, 63, 74)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (0, 16, 9)-net over F₈, using
  - net from sequence [i] based on digital (0, 8)-sequence over F₈, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 0 and N(F) ≥ 9, using
      - the rational function field F₈(x) [i]
    - Niederreiter sequence [i]
2. digital (14, 47, 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]

(30, 30+33, 102)-Net over F₈ — Digital

Digital (30, 63, 102)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(30, 30+33, 3058)-Net in Base 8 — Upper bound on s

There is no (30, 63, 3059)-net in base 8, because

1 times m-reduction [i] would yield (30, 62, 3059)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 98 263402 794397 585178 498270 943038 374741 437484 347162 116139 > 8⁶² [i]