Best Known (48−35, 48, s)-Nets in Base 5
(48−35, 48, 34)-Net over F5 — Constructive and digital
Digital (13, 48, 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]
(48−35, 48, 36)-Net over F5 — Digital
Digital (13, 48, 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
(48−35, 48, 138)-Net in Base 5 — Upper bound on s
There is no (13, 48, 139)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(548, 139, S5, 35), but
- the linear programming bound shows that M ≥ 49 987964 228866 727691 754125 006448 943290 472591 002017 336242 363890 050910 413265 228271 484375 / 13819 112133 980665 153580 918578 384021 333315 861740 228419 > 548 [i]