MinT - Best Known (196−47, 196, s)-Nets in Base 3

Best Known (196−47, 196, s)-Nets in Base 3

(196−47, 196, 464)-Net over F₃ — Constructive and digital

Digital (149, 196, 464)-net over F₃, using

trace code for nets [i] based on digital (2, 49, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(196−47, 196, 990)-Net over F₃ — Digital

Digital (149, 196, 990)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−47, 196, 52287)-Net in Base 3 — Upper bound on s

There is no (149, 196, 52288)-net in base 3, because

1 times m-reduction [i] would yield (149, 195, 52288)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1093 298458 891377 698882 400432 927389 518626 931237 169025 140860 904733 064836 658791 884219 872994 263809 > 3¹⁹⁵ [i]