Best Known (137−128, 137, s)-Nets in Base 5
(137−128, 137, 26)-Net over F5 — Constructive and digital
Digital (9, 137, 26)-net over F5, using
- net from sequence [i] based on digital (9, 25)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 9 and N(F) ≥ 26, using
(137−128, 137, 48)-Net in Base 5 — Upper bound on s
There is no (9, 137, 49)-net in base 5, because
- 42 times m-reduction [i] would yield (9, 95, 49)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(595, 49, S5, 2, 86), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 239 813715 187187 588845 165483 845967 013820 654756 273142 993450 164794 921875 / 87 > 595 [i]
- extracting embedded OOA [i] would yield OOA(595, 49, S5, 2, 86), but