MinT - Best Known (247−59, 247, s)-Nets in Base 3

Best Known (247−59, 247, s)-Nets in Base 3

(247−59, 247, 464)-Net over F₃ — Constructive and digital

Digital (188, 247, 464)-net over F₃, using

1 times m-reduction [i] based on digital (188, 248, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 62, 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]

(247−59, 247, 1215)-Net over F₃ — Digital

Digital (188, 247, 1215)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−59, 247, 65043)-Net in Base 3 — Upper bound on s

There is no (188, 247, 65044)-net in base 3, because

1 times m-reduction [i] would yield (188, 246, 65044)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2354 275671 663903 129999 592706 814744 011274 391183 112855 144465 489507 329570 832818 342824 488974 509243 910395 056423 711608 262025 > 3²⁴⁶ [i]