MinT - Best Known (147−41, 147, s)-Nets in Base 3

Best Known (147−41, 147, s)-Nets in Base 3

(147−41, 147, 252)-Net over F₃ — Constructive and digital

Digital (106, 147, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 49, 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]

(147−41, 147, 439)-Net over F₃ — Digital

Digital (106, 147, 439)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−41, 147, 12606)-Net in Base 3 — Upper bound on s

There is no (106, 147, 12607)-net in base 3, because

1 times m-reduction [i] would yield (106, 146, 12607)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4572 211333 129925 738003 922252 542823 565414 056612 854562 386224 326782 693337 > 3¹⁴⁶ [i]