MinT - Best Known (123−37, 123, s)-Nets in Base 3

Best Known (123−37, 123, s)-Nets in Base 3

(123−37, 123, 192)-Net over F₃ — Constructive and digital

Digital (86, 123, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 41, 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]

(123−37, 123, 293)-Net over F₃ — Digital

Digital (86, 123, 293)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−37, 123, 6452)-Net in Base 3 — Upper bound on s

There is no (86, 123, 6453)-net in base 3, because

1 times m-reduction [i] would yield (86, 122, 6453)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16182 892382 492489 648885 398182 388109 566488 821497 085414 745457 > 3¹²² [i]