MinT - Best Known (98, 98+71, s)-Nets in Base 8

Best Known (98, 98+71, s)-Nets in Base 8

(98, 98+71, 354)-Net over F₈ — Constructive and digital

Digital (98, 169, 354)-net over F₈, using

t-expansion [i] based on digital (93, 169, 354)-net over F₈, using
- 3 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(98, 98+71, 564)-Net over F₈ — Digital

Digital (98, 169, 564)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+71, 42931)-Net in Base 8 — Upper bound on s

There is no (98, 169, 42932)-net in base 8, because

1 times m-reduction [i] would yield (98, 168, 42932)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 52 399118 379601 378136 009062 412949 207293 717779 277165 274069 364491 341327 517218 129155 420364 676215 364671 154957 644042 896101 518258 360453 955785 330501 760347 693917 > 8¹⁶⁸ [i]