MinT - Best Known (66−65, 66, s)-Nets in Base 5

Best Known (66−65, 66, s)-Nets in Base 5

(66−65, 66, 10)-Net over F₅ — Constructive and digital

Digital (1, 66, 10)-net over F₅, using

net from sequence [i] based on digital (1, 9)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 1 and N(F) ≥ 10, using
  - an explicitly constructive algebraic function field [i]

(66−65, 66, 11)-Net in Base 5 — Upper bound on s

There is no (1, 66, 12)-net in base 5, because

55 times m-reduction [i] would yield (1, 11, 12)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5¹¹, 12, S₅, 2, 10), but
  - the linear programming bound for OOAs shows that MÂ â‰¥ 6103 515625 / 121 > 5¹¹ [i]