MinT - Best Known (138, 138+63, s)-Nets in Base 3

Best Known (138, 138+63, s)-Nets in Base 3

(138, 138+63, 192)-Net over F₃ — Constructive and digital

Digital (138, 201, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 67, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(138, 138+63, 388)-Net over F₃ — Digital

Digital (138, 201, 388)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 138+63, 7403)-Net in Base 3 — Upper bound on s

There is no (138, 201, 7404)-net in base 3, because

1 times m-reduction [i] would yield (138, 200, 7404)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 266451 619030 578635 279163 846222 943482 047222 273743 765035 901439 446810 073538 965763 350444 199914 380945 > 3²⁰⁰ [i]