Best Known (84−65, 84, s)-Nets in Base 5
(84−65, 84, 43)-Net over F5 — Constructive and digital
Digital (19, 84, 43)-net over F5, using
- t-expansion [i] based on digital (18, 84, 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
(84−65, 84, 45)-Net over F5 — Digital
Digital (19, 84, 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
(84−65, 84, 108)-Net in Base 5 — Upper bound on s
There is no (19, 84, 109)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(584, 109, S5, 65), but
- the linear programming bound shows that M ≥ 13965 374021 634766 934488 643843 142851 718331 504118 353336 707514 245063 066482 543945 312500 / 257208 127771 599719 537823 > 584 [i]