MinT - Best Known (250−227, 250, s)-Nets in Base 3

Best Known (250−227, 250, s)-Nets in Base 3

(250−227, 250, 32)-Net over F₃ — Constructive and digital

Digital (23, 250, 32)-net over F₃, using

t-expansion [i] based on digital (21, 250, 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]

(250−227, 250, 56)-Net in Base 3 — Upper bound on s

There is no (23, 250, 57)-net in base 3, because

27 times m-reduction [i] would yield (23, 223, 57)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3²²³, 57, S₃, 4, 200), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 2 325534 308593 566841 780398 788839 554570 388150 228976 561478 529410 630953 766257 748117 049334 942846 480672 473864 714911 / 67 > 3²²³ [i]