MinT - Best Known (66, 66+34, s)-Nets in Base 8

Best Known (66, 66+34, s)-Nets in Base 8

(66, 66+34, 368)-Net over F₈ — Constructive and digital

Digital (66, 100, 368)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (1, 18, 14)-net over F₈, using
  - net from sequence [i] based on digital (1, 13)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
      - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
2. digital (48, 82, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 41, 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]

(66, 66+34, 520)-Net in Base 8 — Constructive

(66, 100, 520)-net in base 8, using

base change [i] based on digital (41, 75, 520)-net over F₁₆, using
- 1 times m-reduction [i] based on digital (41, 76, 520)-net over F₁₆, using
  - trace code for nets [i] based on digital (3, 38, 260)-net over F₂₅₆, using
    - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(66, 66+34, 1042)-Net over F₈ — Digital

Digital (66, 100, 1042)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+34, 210435)-Net in Base 8 — Upper bound on s

There is no (66, 100, 210436)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 037064 014664 356396 726465 514977 107126 100641 543124 536769 363282 478099 650728 973486 785735 896864 > 8¹⁰⁰ [i]