MinT - Best Known (144−41, 144, s)-Nets in Base 3

Best Known (144−41, 144, s)-Nets in Base 3

(144−41, 144, 246)-Net over F₃ — Constructive and digital

Digital (103, 144, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 48, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(144−41, 144, 401)-Net over F₃ — Digital

Digital (103, 144, 401)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−41, 144, 10688)-Net in Base 3 — Upper bound on s

There is no (103, 144, 10689)-net in base 3, because

1 times m-reduction [i] would yield (103, 143, 10689)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 169 447855 059114 440174 545958 852724 462047 701624 197226 397899 083579 681169 > 3¹⁴³ [i]