MinT - Best Known (219−66, 219, s)-Nets in Base 3

Best Known (219−66, 219, s)-Nets in Base 3

(219−66, 219, 246)-Net over F₃ — Constructive and digital

Digital (153, 219, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 73, 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]

(219−66, 219, 473)-Net over F₃ — Digital

Digital (153, 219, 473)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−66, 219, 9620)-Net in Base 3 — Upper bound on s

There is no (153, 219, 9621)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 308 912055 319392 616952 585309 951342 863284 202424 399180 221777 603986 001614 678452 186363 177480 521949 320197 024427 > 3²¹⁹ [i]