Best Known (16, 16+39, s)-Nets in Base 5
(16, 16+39, 37)-Net over F5 — Constructive and digital
Digital (16, 55, 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+39, 40)-Net over F5 — Digital
Digital (16, 55, 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+39, 177)-Net in Base 5 — Upper bound on s
There is no (16, 55, 178)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(555, 178, S5, 39), but
- the linear programming bound shows that M ≥ 129528 891661 910196 243633 459864 806229 659887 937133 151434 460887 685418 128967 285156 250000 000000 / 439 613336 040751 796831 131594 618709 092431 449161 340209 > 555 [i]