MinT - Best Known (248−61, 248, s)-Nets in Base 3

Best Known (248−61, 248, s)-Nets in Base 3

(248−61, 248, 400)-Net over F₃ — Constructive and digital

Digital (187, 248, 400)-net over F₃, using

trace code for nets [i] based on digital (1, 62, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(248−61, 248, 1083)-Net over F₃ — Digital

Digital (187, 248, 1083)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−61, 248, 51027)-Net in Base 3 — Upper bound on s

There is no (187, 248, 51028)-net in base 3, because

1 times m-reduction [i] would yield (187, 247, 51028)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7063 571707 800387 256760 019346 187573 604234 644053 974345 521225 763342 783738 618525 443859 548978 470029 747906 686796 673124 176825 > 3²⁴⁷ [i]