Best Known (16, 16+42, s)-Nets in Base 5
(16, 16+42, 37)-Net over F5 — Constructive and digital
Digital (16, 58, 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+42, 40)-Net over F5 — Digital
Digital (16, 58, 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+42, 162)-Net in Base 5 — Upper bound on s
There is no (16, 58, 163)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(558, 163, S5, 42), but
- the linear programming bound shows that M ≥ 810111 164040 136487 609679 121433 873314 027710 260207 654089 958066 056936 604582 006111 741065 979003 906250 000000 / 22 687613 637537 440105 518528 572996 788117 051942 664989 897620 858627 > 558 [i]