MinT - Best Known (234−212, 234, s)-Nets in Base 3

Best Known (234−212, 234, s)-Nets in Base 3

(234−212, 234, 32)-Net over F₃ — Constructive and digital

Digital (22, 234, 32)-net over F₃, using

t-expansion [i] based on digital (21, 234, 32)-net over F₃, using
- net from sequence [i] based on digital (21, 31)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
    - an explicitly constructive algebraic function field [i]

(234−212, 234, 54)-Net in Base 3 — Upper bound on s

There is no (22, 234, 55)-net in base 3, because

19 times m-reduction [i] would yield (22, 215, 55)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3²¹⁵, 55, S₃, 4, 193), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 537 389129 823333 586853 296080 335211 807839 299972 771156 980844 198119 163714 294704 099499 578360 467201 555655 223887 / 97 > 3²¹⁵ [i]