Best Known (65−46, 65, s)-Nets in Base 5
(65−46, 65, 43)-Net over F5 — Constructive and digital
Digital (19, 65, 43)-net over F5, using
- t-expansion [i] based on digital (18, 65, 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
(65−46, 65, 45)-Net over F5 — Digital
Digital (19, 65, 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
(65−46, 65, 199)-Net in Base 5 — Upper bound on s
There is no (19, 65, 200)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(565, 200, S5, 46), but
- the linear programming bound shows that M ≥ 216 267795 608638 086740 636412 023653 078881 270202 611975 370201 299600 115045 404671 310080 857438 151724 636554 718017 578125 / 74663 057688 605915 894535 864885 759226 706353 726858 683534 190094 502253 > 565 [i]