MinT - Best Known (61, 61+27, s)-Nets in Base 3

Best Known (61, 61+27, s)-Nets in Base 3

(61, 61+27, 148)-Net over F₃ — Constructive and digital

Digital (61, 88, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 44, 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]

(61, 61+27, 214)-Net over F₃ — Digital

Digital (61, 88, 214)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+27, 4407)-Net in Base 3 — Upper bound on s

There is no (61, 88, 4408)-net in base 3, because

1 times m-reduction [i] would yield (61, 87, 4408)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 323756 774250 490757 324404 348944 862010 637681 > 3⁸⁷ [i]