Best Known (22, 71, s)-Nets in Base 5
(22, 71, 51)-Net over F5 — Constructive and digital
Digital (22, 71, 51)-net over F5, using
- net from sequence [i] based on digital (22, 50)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 22 and N(F) ≥ 51, using
(22, 71, 250)-Net in Base 5 — Upper bound on s
There is no (22, 71, 251)-net in base 5, because
- 1 times m-reduction [i] would yield (22, 70, 251)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 8 628039 545622 714258 806096 268409 436481 298536 894625 > 570 [i]
- extracting embedded orthogonal array [i] would yield OA(570, 251, S5, 48), but
- the linear programming bound shows that M ≥ 200739 700872 207371 941822 857655 414079 267967 489809 085558 495421 373224 272654 223199 197076 610289 514064 788818 359375 / 22725 681524 131940 245591 201747 442624 808026 373117 483473 863576 > 570 [i]