MinT - Best Known (221−67, 221, s)-Nets in Base 3

Best Known (221−67, 221, s)-Nets in Base 3

(221−67, 221, 228)-Net over F₃ — Constructive and digital

Digital (154, 221, 228)-net over F₃, using

1 times m-reduction [i] based on digital (154, 222, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 74, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(221−67, 221, 468)-Net over F₃ — Digital

Digital (154, 221, 468)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−67, 221, 9947)-Net in Base 3 — Upper bound on s

There is no (154, 221, 9948)-net in base 3, because

1 times m-reduction [i] would yield (154, 220, 9948)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 927 399068 887657 040874 564712 913075 354220 574589 057809 386369 684950 911319 534373 787623 307082 997681 826082 605497 > 3²²⁰ [i]