MinT - Best Known (93, 93+71, s)-Nets in Base 3

Best Known (93, 93+71, s)-Nets in Base 3

(93, 93+71, 80)-Net over F₃ — Constructive and digital

Digital (93, 164, 80)-net over F₃, using

6 times m-reduction [i] based on digital (93, 170, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 85, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(93, 93+71, 126)-Net over F₃ — Digital

Digital (93, 164, 126)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 93+71, 1125)-Net in Base 3 — Upper bound on s

There is no (93, 164, 1126)-net in base 3, because

1 times m-reduction [i] would yield (93, 163, 1126)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 601000 507845 456194 635282 279735 489870 969543 478722 705063 692061 253055 758669 981217 > 3¹⁶³ [i]