Best Known (19, 19+43, s)-Nets in Base 5
(19, 19+43, 43)-Net over F5 — Constructive and digital
Digital (19, 62, 43)-net over F5, using
- t-expansion [i] based on digital (18, 62, 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
(19, 19+43, 45)-Net over F5 — Digital
Digital (19, 62, 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
(19, 19+43, 216)-Net in Base 5 — Upper bound on s
There is no (19, 62, 217)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(562, 217, S5, 43), but
- the linear programming bound shows that M ≥ 32 820355 875686 404771 092800 689258 968771 462569 606632 461420 680013 103004 846186 649956 507608 294486 999511 718750 / 1 488523 332318 283610 530581 404076 081507 725383 791774 568023 305897 > 562 [i]