Best Known (16, 16+44, s)-Nets in Base 5
(16, 16+44, 37)-Net over F5 — Constructive and digital
Digital (16, 60, 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+44, 40)-Net over F5 — Digital
Digital (16, 60, 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+44, 154)-Net in Base 5 — Upper bound on s
There is no (16, 60, 155)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(560, 155, S5, 44), but
- the linear programming bound shows that M ≥ 30139 827251 814202 077560 430516 029504 401126 180225 930150 519674 914744 954230 049541 077031 982006 323570 990823 100146 371871 232986 450195 312500 000000 / 31437 209130 981031 420092 525044 621298 450885 552431 786224 578693 672339 793325 213303 113011 437101 870747 > 560 [i]