MinT - Best Known (213−65, 213, s)-Nets in Base 3

Best Known (213−65, 213, s)-Nets in Base 3

(213−65, 213, 228)-Net over F₃ — Constructive and digital

Digital (148, 213, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 71, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(213−65, 213, 443)-Net over F₃ — Digital

Digital (148, 213, 443)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−65, 213, 9232)-Net in Base 3 — Upper bound on s

There is no (148, 213, 9233)-net in base 3, because

1 times m-reduction [i] would yield (148, 212, 9233)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 141587 413967 380446 811317 145796 020713 202466 756500 920212 155617 592989 202140 094369 736800 930044 090547 693185 > 3²¹² [i]