MinT - Best Known (167, 167+76, s)-Nets in Base 3

Best Known (167, 167+76, s)-Nets in Base 3

(167, 167+76, 204)-Net over F₃ — Constructive and digital

Digital (167, 243, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 81, 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]

(167, 167+76, 461)-Net over F₃ — Digital

Digital (167, 243, 461)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 167+76, 8412)-Net in Base 3 — Upper bound on s

There is no (167, 243, 8413)-net in base 3, because

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]