MinT - Best Known (244−59, 244, s)-Nets in Base 3

Best Known (244−59, 244, s)-Nets in Base 3

(244−59, 244, 464)-Net over F₃ — Constructive and digital

Digital (185, 244, 464)-net over F₃, using

trace code for nets [i] based on digital (2, 61, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(244−59, 244, 1144)-Net over F₃ — Digital

Digital (185, 244, 1144)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−59, 244, 58053)-Net in Base 3 — Upper bound on s

There is no (185, 244, 58054)-net in base 3, because

1 times m-reduction [i] would yield (185, 243, 58054)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 225510 259432 171574 011903 528712 189298 823805 291901 970488 642667 893459 866488 667327 238775 699011 336247 122005 954491 971381 > 3²⁴³ [i]