MinT - Best Known (214−63, 214, s)-Nets in Base 3

Best Known (214−63, 214, s)-Nets in Base 3

(214−63, 214, 252)-Net over F₃ — Constructive and digital

Digital (151, 214, 252)-net over F₃, using

3¹ times duplication [i] based on digital (150, 213, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 71, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(214−63, 214, 499)-Net over F₃ — Digital

Digital (151, 214, 499)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−63, 214, 11753)-Net in Base 3 — Upper bound on s

There is no (151, 214, 11754)-net in base 3, because

1 times m-reduction [i] would yield (151, 213, 11754)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 424147 046965 378911 261485 519468 709719 625370 131550 774941 016554 191737 491566 017681 422322 770562 035850 279641 > 3²¹³ [i]