Best Known (139−128, 139, s)-Nets in Base 5
(139−128, 139, 32)-Net over F5 — Constructive and digital
Digital (11, 139, 32)-net over F5, using
- net from sequence [i] based on digital (11, 31)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using
(139−128, 139, 57)-Net in Base 5 — Upper bound on s
There is no (11, 139, 58)-net in base 5, because
- 26 times m-reduction [i] would yield (11, 113, 58)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5113, 58, S5, 2, 102), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1107 409718 022660 615507 187316 986333 208159 408447 723848 212262 964807 450771 331787 109375 / 103 > 5113 [i]
- extracting embedded OOA [i] would yield OOA(5113, 58, S5, 2, 102), but