MinT - Best Known (91, 91+57, s)-Nets in Base 3

Best Known (91, 91+57, s)-Nets in Base 3

(91, 91+57, 148)-Net over F₃ — Constructive and digital

Digital (91, 148, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 74, 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]

(91, 91+57, 161)-Net over F₃ — Digital

Digital (91, 148, 161)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+57, 1779)-Net in Base 3 — Upper bound on s

There is no (91, 148, 1780)-net in base 3, because

1 times m-reduction [i] would yield (91, 147, 1780)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13858 773174 041311 387848 083824 576453 865786 289740 581954 892093 022813 688065 > 3¹⁴⁷ [i]