MinT - Best Known (92, 92+81, s)-Nets in Base 8

Best Known (92, 92+81, s)-Nets in Base 8

(92, 92+81, 256)-Net over F₈ — Constructive and digital

Digital (92, 173, 256)-net over F₈, using

8¹ times duplication [i] based on digital (91, 172, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 86, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(92, 92+81, 362)-Net over F₈ — Digital

Digital (92, 173, 362)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(92, 92+81, 17192)-Net in Base 8 — Upper bound on s

There is no (92, 173, 17193)-net in base 8, because

1 times m-reduction [i] would yield (92, 172, 17193)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 214678 973968 614476 740613 269000 074676 648288 293838 533960 906037 121814 191693 131625 222089 667797 734958 544695 383755 699953 759839 200198 082221 607860 939393 308050 491305 > 8¹⁷² [i]