Best Known (18, 18+46, s)-Nets in Base 5
(18, 18+46, 43)-Net over F5 — Constructive and digital
Digital (18, 64, 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]
(18, 18+46, 180)-Net in Base 5 — Upper bound on s
There is no (18, 64, 181)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(564, 181, S5, 46), but
- the linear programming bound shows that M ≥ 1 117996 832565 723353 881257 291682 456247 480245 045336 996365 538220 617353 152438 464016 309119 543123 501283 599097 178012 016229 331493 377685 546875 / 1918 894296 622802 775599 627416 639747 490464 678176 704125 231717 373057 475326 476989 891630 259679 > 564 [i]