MinT - Best Known (173−100, 173, s)-Nets in Base 8

Best Known (173−100, 173, s)-Nets in Base 8

(173−100, 173, 110)-Net over F₈ — Constructive and digital

Digital (73, 173, 110)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (9, 59, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]
2. digital (14, 114, 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]

(173−100, 173, 155)-Net over F₈ — Digital

Digital (73, 173, 155)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−100, 173, 161)-Net in Base 8

(73, 173, 161)-net in base 8, using

8¹ times duplication [i] based on (72, 172, 161)-net in base 8, using
- base change [i] based on digital (29, 129, 161)-net over F₁₆, using
  - net from sequence [i] based on digital (29, 160)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 29 and N(F) ≥ 161, using
      - a curve from the manYPoints database [i]

(173−100, 173, 3677)-Net in Base 8 — Upper bound on s

There is no (73, 173, 3678)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 729633 039505 920241 514077 251440 061571 986317 603380 945938 306227 975501 216546 304205 330592 992345 861517 929273 197884 182902 068394 625497 697023 132386 695528 382047 415012 > 8¹⁷³ [i]