MinT - Best Known (144−38, 144, s)-Nets in Base 3

Best Known (144−38, 144, s)-Nets in Base 3

(144−38, 144, 282)-Net over F₃ — Constructive and digital

Digital (106, 144, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 48, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(144−38, 144, 531)-Net over F₃ — Digital

Digital (106, 144, 531)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−38, 144, 16359)-Net in Base 3 — Upper bound on s

There is no (106, 144, 16360)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 507 784299 592510 871571 250244 584250 140212 901408 557660 750074 639591 947041 > 3¹⁴⁴ [i]