Best Known (16, 16+57, s)-Nets in Base 5
(16, 16+57, 37)-Net over F5 — Constructive and digital
Digital (16, 73, 37)-net over F5, using
- net from sequence [i] based on digital (16, 36)-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 5 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]
(16, 16+57, 40)-Net over F5 — Digital
Digital (16, 73, 40)-net over F5, using
- net from sequence [i] based on digital (16, 39)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 16 and N(F) ≥ 40, using
(16, 16+57, 92)-Net in Base 5 — Upper bound on s
There is no (16, 73, 93)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(573, 93, S5, 57), but
- the linear programming bound shows that M ≥ 127 452437 670341 469827 097542 928673 323814 336981 740780 174732 208251 953125 / 111510 311731 703742 > 573 [i]