MinT - Best Known (198−61, 198, s)-Nets in Base 3

Best Known (198−61, 198, s)-Nets in Base 3

(198−61, 198, 204)-Net over F₃ — Constructive and digital

Digital (137, 198, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 66, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(198−61, 198, 404)-Net over F₃ — Digital

Digital (137, 198, 404)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−61, 198, 8152)-Net in Base 3 — Upper bound on s

There is no (137, 198, 8153)-net in base 3, because

1 times m-reduction [i] would yield (137, 197, 8153)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9857 109522 233429 095253 472771 882811 446829 047099 502511 619575 483408 332638 773169 107740 331775 375785 > 3¹⁹⁷ [i]