Best Known (64−45, 64, s)-Nets in Base 5
(64−45, 64, 43)-Net over F5 — Constructive and digital
Digital (19, 64, 43)-net over F5, using
- t-expansion [i] based on digital (18, 64, 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
(64−45, 64, 45)-Net over F5 — Digital
Digital (19, 64, 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
(64−45, 64, 203)-Net in Base 5 — Upper bound on s
There is no (19, 64, 204)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(564, 204, S5, 45), but
- the linear programming bound shows that M ≥ 2 232899 961702 667680 521795 148663 127762 338126 641981 965951 657221 910765 681029 875651 120164 548046 886920 928955 078125 / 3968 894816 478051 920029 715098 018741 844819 963703 215694 770504 293666 > 564 [i]