Best Known (86−65, 86, s)-Nets in Base 5
(86−65, 86, 43)-Net over F5 — Constructive and digital
Digital (21, 86, 43)-net over F5, using
- t-expansion [i] based on digital (18, 86, 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
(86−65, 86, 50)-Net over F5 — Digital
Digital (21, 86, 50)-net over F5, using
- net from sequence [i] based on digital (21, 49)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 21 and N(F) ≥ 50, using
(86−65, 86, 144)-Net in Base 5 — Upper bound on s
There is no (21, 86, 145)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(586, 145, S5, 65), but
- the linear programming bound shows that M ≥ 1 681971 586304 181223 187907 190141 264188 172812 749344 276629 843014 476462 881651 126808 966524 933987 666420 440086 867329 609762 499671 015636 681116 117777 216867 334999 506056 192331 016063 690185 546875 / 1 235197 506395 108210 300700 030853 409382 253498 637886 138574 180390 146599 149915 868081 543662 842688 306834 854616 250416 282850 014131 > 586 [i]