Best Known (13, 50, s)-Nets in Base 5
(13, 50, 34)-Net over F5 — Constructive and digital
Digital (13, 50, 34)-net over F5, using
- net from sequence [i] based on digital (13, 33)-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 2 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]
(13, 50, 36)-Net over F5 — Digital
Digital (13, 50, 36)-net over F5, using
- net from sequence [i] based on digital (13, 35)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 13 and N(F) ≥ 36, using
(13, 50, 130)-Net in Base 5 — Upper bound on s
There is no (13, 50, 131)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(550, 131, S5, 37), but
- the linear programming bound shows that M ≥ 181 651510 656125 428709 780769 114056 406925 319677 471762 696247 846596 689105 126642 971299 588680 267333 984375 / 1934 822153 377187 405051 876229 575941 603854 391958 132931 137567 207323 > 550 [i]