Best Known (72−46, 72, s)-Nets in Base 3
(72−46, 72, 36)-Net over F3 — Constructive and digital
Digital (26, 72, 36)-net over F3, using
- net from sequence [i] based on digital (26, 35)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using
(72−46, 72, 37)-Net over F3 — Digital
Digital (26, 72, 37)-net over F3, using
- net from sequence [i] based on digital (26, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 25, N(F) = 36, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 25 and N(F) ≥ 36, using algebraic function fields over ℤ3 by Niederreiter/Xing [i]
(72−46, 72, 96)-Net in Base 3 — Upper bound on s
There is no (26, 72, 97)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(372, 97, S3, 46), but
- the linear programming bound shows that M ≥ 27848 335335 870397 950530 479039 339751 613066 604593 / 1 016088 552625 > 372 [i]