MinT - Best Known (100, 100+49, s)-Nets in Base 8

Best Known (100, 100+49, s)-Nets in Base 8

(100, 100+49, 402)-Net over F₈ — Constructive and digital

Digital (100, 149, 402)-net over F₈, using

1 times m-reduction [i] based on digital (100, 150, 402)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 36, 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 (64, 114, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 57, 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]

(100, 100+49, 576)-Net in Base 8 — Constructive

(100, 149, 576)-net in base 8, using

9 times m-reduction [i] based on (100, 158, 576)-net in base 8, using
- trace code for nets [i] based on (21, 79, 288)-net in base 64, using
  - 5 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]

(100, 100+49, 1726)-Net over F₈ — Digital

Digital (100, 149, 1726)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 100+49, 519167)-Net in Base 8 — Upper bound on s

There is no (100, 149, 519168)-net in base 8, because

1 times m-reduction [i] would yield (100, 148, 519168)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 429397 779883 032482 388660 186073 372913 085119 909674 547201 588693 312283 342070 396219 244731 708722 703825 974164 943719 867916 554278 527371 584577 > 8¹⁴⁸ [i]