Best Known (82−66, 82, s)-Nets in Base 5
(82−66, 82, 37)-Net over F5 — Constructive and digital
Digital (16, 82, 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]
(82−66, 82, 40)-Net over F5 — Digital
Digital (16, 82, 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
(82−66, 82, 87)-Net in Base 5 — Upper bound on s
There is no (16, 82, 88)-net in base 5, because
- 3 times m-reduction [i] would yield (16, 79, 88)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(579, 88, S5, 63), but
- the linear programming bound shows that M ≥ 2 305765 957491 564643 704051 729145 021454 314701 259136 199951 171875 / 132202 > 579 [i]
- extracting embedded orthogonal array [i] would yield OA(579, 88, S5, 63), but