Best Known (70−51, 70, s)-Nets in Base 5
(70−51, 70, 43)-Net over F5 — Constructive and digital
Digital (19, 70, 43)-net over F5, using
- t-expansion [i] based on digital (18, 70, 43)-net over F5, using
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 17, N(F) = 42, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
(70−51, 70, 45)-Net over F5 — Digital
Digital (19, 70, 45)-net over F5, using
- net from sequence [i] based on digital (19, 44)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 19 and N(F) ≥ 45, using
(70−51, 70, 189)-Net in Base 5 — Upper bound on s
There is no (19, 70, 190)-net in base 5, because
- 3 times m-reduction [i] would yield (19, 67, 190)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(567, 190, S5, 48), but
- the linear programming bound shows that M ≥ 139 124959 067603 873322 973848 261999 902938 721401 487962 196427 958905 932685 857275 222943 487399 518687 652744 119986 891746 520996 093750 000000 000000 / 1945 405900 784912 155706 111127 555122 141815 117656 438746 607270 389576 779617 403604 841411 250557 > 567 [i]
- extracting embedded orthogonal array [i] would yield OA(567, 190, S5, 48), but