MinT - Best Known (211−63, 211, s)-Nets in Base 3

Best Known (211−63, 211, s)-Nets in Base 3

(211−63, 211, 246)-Net over F₃ — Constructive and digital

Digital (148, 211, 246)-net over F₃, using

3¹ times duplication [i] based on digital (147, 210, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 70, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(211−63, 211, 471)-Net over F₃ — Digital

Digital (148, 211, 471)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−63, 211, 10564)-Net in Base 3 — Upper bound on s

There is no (148, 211, 10565)-net in base 3, because

1 times m-reduction [i] would yield (148, 210, 10565)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15690 135094 931823 645448 699106 322721 015808 331505 433147 164723 412484 099504 733350 983926 355426 834536 780219 > 3²¹⁰ [i]