MinT - Best Known (66, 66+81, s)-Nets in Base 8

Best Known (66, 66+81, s)-Nets in Base 8

(66, 66+81, 113)-Net over F₈ — Constructive and digital

Digital (66, 147, 113)-net over F₈, using

1 times m-reduction [i] based on digital (66, 148, 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, 96, 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]

(66, 66+81, 162)-Net over F₈ — Digital

Digital (66, 147, 162)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+81, 4431)-Net in Base 8 — Upper bound on s

There is no (66, 147, 4432)-net in base 8, because

1 times m-reduction [i] would yield (66, 146, 4432)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 715562 997661 931040 518415 808056 566354 061083 937946 394557 479938 465185 715125 263038 507644 801992 056102 093980 888656 177316 833579 747084 906402 > 8¹⁴⁶ [i]