MinT - Best Known (247−77, 247, s)-Nets in Base 3

Best Known (247−77, 247, s)-Nets in Base 3

(247−77, 247, 204)-Net over F₃ — Constructive and digital

Digital (170, 247, 204)-net over F₃, using

3¹ times duplication [i] based on digital (169, 246, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 82, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(247−77, 247, 472)-Net over F₃ — Digital

Digital (170, 247, 472)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−77, 247, 9177)-Net in Base 3 — Upper bound on s

There is no (170, 247, 9178)-net in base 3, because

1 times m-reduction [i] would yield (170, 246, 9178)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2356 263302 152921 773640 381421 652664 997544 674096 495356 821890 073627 197084 783468 018161 049763 053135 990167 682314 169157 743373 > 3²⁴⁶ [i]