MinT - Best Known (167, 167+77, s)-Nets in Base 3

Best Known (167, 167+77, s)-Nets in Base 3

(167, 167+77, 192)-Net over F₃ — Constructive and digital

Digital (167, 244, 192)-net over F₃, using

3¹ times duplication [i] based on digital (166, 243, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 81, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(167, 167+77, 449)-Net over F₃ — Digital

Digital (167, 244, 449)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 167+77, 8412)-Net in Base 3 — Upper bound on s

There is no (167, 244, 8413)-net in base 3, because

1 times m-reduction [i] would yield (167, 243, 8413)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 501479 509912 444840 970963 275737 249331 158649 312648 537611 784986 423570 054954 472390 611257 082459 291215 157860 562280 822065 > 3²⁴³ [i]