Best Known (26, 26+44, s)-Nets in Base 3
(26, 26+44, 36)-Net over F3 — Constructive and digital
Digital (26, 70, 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
(26, 26+44, 37)-Net over F3 — Digital
Digital (26, 70, 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]
(26, 26+44, 104)-Net in Base 3 — Upper bound on s
There is no (26, 70, 105)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(370, 105, S3, 44), but
- the linear programming bound shows that M ≥ 6510 936616 779271 177570 198314 871304 018934 800295 922451 627877 / 2 398681 054634 692754 093750 > 370 [i]