MinT - Best Known (244−73, 244, s)-Nets in Base 3

Best Known (244−73, 244, s)-Nets in Base 3

(244−73, 244, 252)-Net over F₃ — Constructive and digital

Digital (171, 244, 252)-net over F₃, using

3¹ times duplication [i] based on digital (170, 243, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 81, 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]

(244−73, 244, 532)-Net over F₃ — Digital

Digital (171, 244, 532)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−73, 244, 11829)-Net in Base 3 — Upper bound on s

There is no (171, 244, 11830)-net in base 3, because

1 times m-reduction [i] would yield (171, 243, 11830)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 253710 301331 001107 487016 690526 115049 207395 404881 979527 197042 978444 779164 060830 427934 222165 642642 410807 896120 359241 > 3²⁴³ [i]