MinT - Best Known (90, 90+83, s)-Nets in Base 8

Best Known (90, 90+83, s)-Nets in Base 8

(90, 90+83, 208)-Net over F₈ — Constructive and digital

Digital (90, 173, 208)-net over F₈, using

8¹ times duplication [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]

(90, 90+83, 225)-Net in Base 8 — Constructive

(90, 173, 225)-net in base 8, using

8¹ times duplication [i] based on (89, 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]

(90, 90+83, 327)-Net over F₈ — Digital

Digital (90, 173, 327)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+83, 14144)-Net in Base 8 — Upper bound on s

There is no (90, 173, 14145)-net in base 8, because

1 times m-reduction [i] would yield (90, 172, 14145)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 214690 866231 933218 642741 682520 310219 371889 980486 043460 163543 234654 328014 521559 934067 513321 775095 642590 571368 838086 634180 748916 086929 056276 417213 550202 615680 > 8¹⁷² [i]