Best Known (69−43, 69, s)-Nets in Base 3
(69−43, 69, 36)-Net over F3 — Constructive and digital
Digital (26, 69, 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
(69−43, 69, 37)-Net over F3 — Digital
Digital (26, 69, 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]
(69−43, 69, 109)-Net in Base 3 — Upper bound on s
There is no (26, 69, 110)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(369, 110, S3, 43), but
- the linear programming bound shows that M ≥ 50 201668 479718 874895 499466 390708 573652 199787 057298 328076 392048 487469 / 56580 236789 640752 964425 611289 453125 > 369 [i]