Best Known (57−42, 57, s)-Nets in Base 5
(57−42, 57, 36)-Net over F5 — Constructive and digital
Digital (15, 57, 36)-net over F5, using
- net from sequence [i] based on digital (15, 35)-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 4 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]
(57−42, 57, 39)-Net over F5 — Digital
Digital (15, 57, 39)-net over F5, using
- t-expansion [i] based on digital (14, 57, 39)-net over F5, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 14 and N(F) ≥ 39, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
(57−42, 57, 144)-Net in Base 5 — Upper bound on s
There is no (15, 57, 145)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(557, 145, S5, 42), but
- the linear programming bound shows that M ≥ 12767 367763 100081 691395 828743 427028 269216 988812 694493 147537 550295 718605 334325 184032 888794 011325 170885 129409 725777 804851 531982 421875 / 1 737109 351988 699920 911630 471359 423721 738096 848085 001018 934875 932768 560368 300697 472898 056968 > 557 [i]