MinT - Best Known (210−186, 210, s)-Nets in Base 3

Best Known (210−186, 210, s)-Nets in Base 3

(210−186, 210, 32)-Net over F₃ — Constructive and digital

Digital (24, 210, 32)-net over F₃, using

t-expansion [i] based on digital (21, 210, 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]

(210−186, 210, 59)-Net in Base 3 — Upper bound on s

There is no (24, 210, 60)-net in base 3, because

35 times m-reduction [i] would yield (24, 175, 60)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁷⁵, 60, S₃, 3, 151), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 8 464149 782874 043593 254414 191179 506861 158311 266932 799636 000173 971661 904149 225893 113289 / 19 > 3¹⁷⁵ [i]