MinT - Best Known (148−49, 148, s)-Nets in Base 8

Best Known (148−49, 148, s)-Nets in Base 8

(148−49, 148, 402)-Net over F₈ — Constructive and digital

Digital (99, 148, 402)-net over F₈, using

8¹ times duplication [i] based on digital (98, 147, 402)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 35, 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 (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]

(148−49, 148, 576)-Net in Base 8 — Constructive

(99, 148, 576)-net in base 8, using

t-expansion [i] based on (97, 148, 576)-net in base 8, using
- 6 times m-reduction [i] based on (97, 154, 576)-net in base 8, using
  - trace code for nets [i] based on (20, 77, 288)-net in base 64, using
    - base change [i] based on digital (9, 66, 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]

(148−49, 148, 1654)-Net over F₈ — Digital

Digital (99, 148, 1654)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−49, 148, 476077)-Net in Base 8 — Upper bound on s

There is no (99, 148, 476078)-net in base 8, because

1 times m-reduction [i] would yield (99, 147, 476078)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 678698 735930 417442 296403 797214 036770 695157 299043 611972 802680 641769 433128 869298 659755 053424 334508 661095 999125 274150 441518 200831 969774 > 8¹⁴⁷ [i]