Best Known (12, 12+123, s)-Nets in Base 5
(12, 12+123, 33)-Net over F5 — Constructive and digital
Digital (12, 135, 33)-net over F5, using
- net from sequence [i] based on digital (12, 32)-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 1 place 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]
(12, 12+123, 62)-Net in Base 5 — Upper bound on s
There is no (12, 135, 63)-net in base 5, because
- 12 times m-reduction [i] would yield (12, 123, 63)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5123, 63, S5, 2, 111), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 470 197740 328915 003187 494614 888898 271127 466222 708835 008603 500682 511366 903781 890869 140625 / 4 > 5123 [i]
- extracting embedded OOA [i] would yield OOA(5123, 63, S5, 2, 111), but