MinT - Best Known (101, 101+37, s)-Nets in Base 3

Best Known (101, 101+37, s)-Nets in Base 3

(101, 101+37, 264)-Net over F₃ — Constructive and digital

Digital (101, 138, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 46, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(101, 101+37, 484)-Net over F₃ — Digital

Digital (101, 138, 484)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+37, 16145)-Net in Base 3 — Upper bound on s

There is no (101, 138, 16146)-net in base 3, because

1 times m-reduction [i] would yield (101, 137, 16146)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 232184 061468 535805 258342 124446 030489 702269 223732 407715 027336 753557 > 3¹³⁷ [i]