MinT - Best Known (76, 76+73, s)-Nets in Base 9

Best Known (76, 76+73, s)-Nets in Base 9

(76, 76+73, 200)-Net over F₉ — Constructive and digital

Digital (76, 149, 200)-net over F₉, using

1 times m-reduction [i] based on digital (76, 150, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 75, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(76, 76+73, 300)-Net over F₉ — Digital

Digital (76, 149, 300)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+73, 14928)-Net in Base 9 — Upper bound on s

There is no (76, 149, 14929)-net in base 9, because

1 times m-reduction [i] would yield (76, 148, 14929)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1693 647835 446091 293783 069136 726114 538127 149787 705858 356802 958832 326046 379201 762165 458031 644557 591398 744252 879404 708419 402204 521160 600207 074465 > 9¹⁴⁸ [i]