Best Known (87−66, 87, s)-Nets in Base 5
(87−66, 87, 43)-Net over F5 — Constructive and digital
Digital (21, 87, 43)-net over F5, using
- t-expansion [i] based on digital (18, 87, 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
(87−66, 87, 50)-Net over F5 — Digital
Digital (21, 87, 50)-net over F5, using
- net from sequence [i] based on digital (21, 49)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 21 and N(F) ≥ 50, using
(87−66, 87, 138)-Net in Base 5 — Upper bound on s
There is no (21, 87, 139)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(587, 139, S5, 66), but
- the linear programming bound shows that M ≥ 314911 252589 678982 955592 780437 601790 628234 495165 860083 330703 714374 904486 804017 335988 909319 527191 308599 883834 418164 951785 001903 772354 125976 562500 / 48451 357963 877144 544304 960539 357735 094650 902841 329614 666232 431720 811360 463254 002671 > 587 [i]