MinT - Best Known (173−82, 173, s)-Nets in Base 8

Best Known (173−82, 173, s)-Nets in Base 8

(173−82, 173, 208)-Net over F₈ — Constructive and digital

Digital (91, 173, 208)-net over F₈, using

8¹ times duplication [i] based on digital (90, 172, 208)-net over F₈, using
- t-expansion [i] based on digital (89, 172, 208)-net over F₈, using
  - trace code for nets [i] based on digital (3, 86, 104)-net over F₆₄, using
    - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(173−82, 173, 225)-Net in Base 8 — Constructive

(91, 173, 225)-net in base 8, using

8¹ times duplication [i] based on (90, 172, 225)-net in base 8, using
- t-expansion [i] based on (83, 172, 225)-net in base 8, using
  - base change [i] based on digital (40, 129, 225)-net over F₁₆, using
    - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
        a function field by GarcÃa and Quoos [i]

(173−82, 173, 344)-Net over F₈ — Digital

Digital (91, 173, 344)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−82, 173, 14881)-Net in Base 8 — Upper bound on s

There is no (91, 173, 14882)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 716320 980995 197957 115865 536230 685951 539380 547351 196917 541367 349179 020125 030939 413278 081305 487856 100996 359718 743020 195969 695065 289441 510498 742241 746743 108160 > 8¹⁷³ [i]