Best Known (128−110, 128, s)-Nets in Base 5
(128−110, 128, 43)-Net over F5 — Constructive and digital
Digital (18, 128, 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]
(128−110, 128, 97)-Net in Base 5 — Upper bound on s
There is no (18, 128, 98)-net in base 5, because
- 42 times m-reduction [i] would yield (18, 86, 98)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(586, 98, S5, 68), but
- the linear programming bound shows that M ≥ 874 729765 284188 678803 006084 493121 274903 160156 100057 065486 907958 984375 / 543 471687 > 586 [i]
- extracting embedded orthogonal array [i] would yield OA(586, 98, S5, 68), but