MinT - Best Known (169, 169+71, s)-Nets in Base 3

Best Known (169, 169+71, s)-Nets in Base 3

(169, 169+71, 264)-Net over F₃ — Constructive and digital

Digital (169, 240, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 80, 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]

(169, 169+71, 544)-Net over F₃ — Digital

Digital (169, 240, 544)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169, 169+71, 12563)-Net in Base 3 — Upper bound on s

There is no (169, 240, 12564)-net in base 3, because

1 times m-reduction [i] would yield (169, 239, 12564)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 078770 508417 281327 243603 382357 583018 196160 794513 377717 125670 923344 633856 626896 236172 262282 615359 266834 525118 784369 > 3²³⁹ [i]