Best Known (49−36, 49, s)-Nets in Base 5
(49−36, 49, 34)-Net over F5 — Constructive and digital
Digital (13, 49, 34)-net over F5, using
- net from sequence [i] based on digital (13, 33)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 2 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(49−36, 49, 36)-Net over F5 — Digital
Digital (13, 49, 36)-net over F5, using
- net from sequence [i] based on digital (13, 35)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 13 and N(F) ≥ 36, using
(49−36, 49, 133)-Net in Base 5 — Upper bound on s
There is no (13, 49, 134)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(549, 134, S5, 36), but
- the linear programming bound shows that M ≥ 73 609391 775390 825320 757199 013536 957676 467943 589674 422999 777598 306536 674499 511718 750000 / 4032 505493 837619 457597 508533 708691 849004 692896 785209 > 549 [i]