MinT - Best Known (228−97, 228, s)-Nets in Base 3

Best Known (228−97, 228, s)-Nets in Base 3

(228−97, 228, 148)-Net over F₃ — Constructive and digital

Digital (131, 228, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 114, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(228−97, 228, 176)-Net over F₃ — Digital

Digital (131, 228, 176)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−97, 228, 1644)-Net in Base 3 — Upper bound on s

There is no (131, 228, 1645)-net in base 3, because

1 times m-reduction [i] would yield (131, 227, 1645)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 080453 121643 495994 408669 084758 864627 472898 345747 664268 910404 458713 442353 815004 320640 576952 306287 264040 519489 > 3²²⁷ [i]