MinT - Best Known (213−67, 213, s)-Nets in Base 3

Best Known (213−67, 213, s)-Nets in Base 3

(213−67, 213, 192)-Net over F₃ — Constructive and digital

Digital (146, 213, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 71, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(213−67, 213, 404)-Net over F₃ — Digital

Digital (146, 213, 404)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−67, 213, 7614)-Net in Base 3 — Upper bound on s

There is no (146, 213, 7615)-net in base 3, because

1 times m-reduction [i] would yield (146, 212, 7615)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 141690 034713 837934 073993 151219 377679 824092 115241 489205 656326 125846 705173 066924 606832 209671 554420 095807 > 3²¹² [i]