Best Known (81−62, 81, s)-Nets in Base 5
(81−62, 81, 43)-Net over F5 — Constructive and digital
Digital (19, 81, 43)-net over F5, using
- t-expansion [i] based on digital (18, 81, 43)-net over F5, using
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 17, N(F) = 42, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
(81−62, 81, 45)-Net over F5 — Digital
Digital (19, 81, 45)-net over F5, using
- net from sequence [i] based on digital (19, 44)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 19 and N(F) ≥ 45, using
(81−62, 81, 121)-Net in Base 5 — Upper bound on s
There is no (19, 81, 122)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(581, 122, S5, 62), but
- the linear programming bound shows that M ≥ 17133 810176 112946 923079 960994 186207 668494 350258 022665 566660 526340 926617 994142 588941 031135 618686 676025 390625 / 38 859193 036377 505043 562669 624921 157068 985448 566497 > 581 [i]