Best Known (72−56, 72, s)-Nets in Base 5
(72−56, 72, 37)-Net over F5 — Constructive and digital
Digital (16, 72, 37)-net over F5, using
- net from sequence [i] based on digital (16, 36)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 5 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(72−56, 72, 40)-Net over F5 — Digital
Digital (16, 72, 40)-net over F5, using
- net from sequence [i] based on digital (16, 39)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 16 and N(F) ≥ 40, using
(72−56, 72, 96)-Net in Base 5 — Upper bound on s
There is no (16, 72, 97)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(572, 97, S5, 56), but
- the linear programming bound shows that M ≥ 7 089744 942695 552122 204900 763230 601967 723742 973248 590715 229511 260986 328125 / 27015 220325 499280 550676 > 572 [i]