MinT - Best Known (126, 126+85, s)-Nets in Base 3

Best Known (126, 126+85, s)-Nets in Base 3

(126, 126+85, 148)-Net over F₃ — Constructive and digital

Digital (126, 211, 148)-net over F₃, using

7 times m-reduction [i] based on digital (126, 218, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 109, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(126, 126+85, 192)-Net over F₃ — Digital

Digital (126, 211, 192)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+85, 1965)-Net in Base 3 — Upper bound on s

There is no (126, 211, 1966)-net in base 3, because

1 times m-reduction [i] would yield (126, 210, 1966)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15991 782589 040262 228279 973863 717290 660394 456426 862512 630780 619410 597613 609566 970384 813549 012210 555245 > 3²¹⁰ [i]