MinT - Best Known (111, 111+77, s)-Nets in Base 3

Best Known (111, 111+77, s)-Nets in Base 3

(111, 111+77, 148)-Net over F₃ — Constructive and digital

Digital (111, 188, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 94, 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]

(111, 111+77, 166)-Net over F₃ — Digital

Digital (111, 188, 166)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+77, 1636)-Net in Base 3 — Upper bound on s

There is no (111, 188, 1637)-net in base 3, because

1 times m-reduction [i] would yield (111, 187, 1637)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 167818 756959 184989 194203 247993 370042 127359 099002 740306 910425 681976 950056 038968 464081 641601 > 3¹⁸⁷ [i]