MinT - Best Known (154, 154+65, s)-Nets in Base 3

Best Known (154, 154+65, s)-Nets in Base 3

(154, 154+65, 252)-Net over F₃ — Constructive and digital

Digital (154, 219, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 73, 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]

(154, 154+65, 496)-Net over F₃ — Digital

Digital (154, 219, 496)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 154+65, 11351)-Net in Base 3 — Upper bound on s

There is no (154, 219, 11352)-net in base 3, because

1 times m-reduction [i] would yield (154, 218, 11352)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 103 173864 307991 960712 259654 307196 670575 704374 231634 769319 768554 597176 228872 482233 768078 211385 920090 847233 > 3²¹⁸ [i]