Best Known (126−105, 126, s)-Nets in Base 5
(126−105, 126, 43)-Net over F5 — Constructive and digital
Digital (21, 126, 43)-net over F5, using
- t-expansion [i] based on digital (18, 126, 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
(126−105, 126, 50)-Net over F5 — Digital
Digital (21, 126, 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
(126−105, 126, 111)-Net in Base 5 — Upper bound on s
There is no (21, 126, 112)-net in base 5, because
- 29 times m-reduction [i] would yield (21, 97, 112)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(597, 112, S5, 76), but
- the linear programming bound shows that M ≥ 29 282971 382900 591824 936232 851882 769051 034272 056455 165511 579252 779483 795166 015625 / 409917 357801 > 597 [i]
- extracting embedded orthogonal array [i] would yield OA(597, 112, S5, 76), but