MinT - Best Known (148−47, 148, s)-Nets in Base 8

Best Known (148−47, 148, s)-Nets in Base 8

(148−47, 148, 419)-Net over F₈ — Constructive and digital

Digital (101, 148, 419)-net over F₈, using

2 times m-reduction [i] based on digital (101, 150, 419)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 38, 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]
  2. digital (63, 112, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 56, 177)-net over F₆₄, using
      - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(148−47, 148, 576)-Net in Base 8 — Constructive

(101, 148, 576)-net in base 8, using

12 times m-reduction [i] based on (101, 160, 576)-net in base 8, using
- trace code for nets [i] based on (21, 80, 288)-net in base 64, using
  - 4 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
    - base change [i] based on digital (9, 72, 288)-net over F₁₂₈, using
      - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(148−47, 148, 2092)-Net over F₈ — Digital

Digital (101, 148, 2092)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−47, 148, 796660)-Net in Base 8 — Upper bound on s

There is no (101, 148, 796661)-net in base 8, because

1 times m-reduction [i] would yield (101, 147, 796661)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 678471 114927 880133 530122 756238 223104 517325 958506 994066 115641 548155 503993 438559 472246 654259 422519 281124 852647 980720 273944 401881 226208 > 8¹⁴⁷ [i]