MinT - Best Known (216−68, 216, s)-Nets in Base 3

Best Known (216−68, 216, s)-Nets in Base 3

(216−68, 216, 192)-Net over F₃ — Constructive and digital

Digital (148, 216, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 72, 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]

(216−68, 216, 408)-Net over F₃ — Digital

Digital (148, 216, 408)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−68, 216, 7237)-Net in Base 3 — Upper bound on s

There is no (148, 216, 7238)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 479974 874007 327871 340715 600250 377946 654686 813096 898849 081568 211383 046435 207677 079371 127911 304029 713453 > 3²¹⁶ [i]