Best Known (27, 86, s)-Nets in Base 5
(27, 86, 51)-Net over F5 — Constructive and digital
Digital (27, 86, 51)-net over F5, using
- t-expansion [i] based on digital (22, 86, 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
- net from sequence [i] based on digital (22, 50)-sequence over F5, using
(27, 86, 55)-Net over F5 — Digital
Digital (27, 86, 55)-net over F5, using
- t-expansion [i] based on digital (23, 86, 55)-net over F5, using
- net from sequence [i] based on digital (23, 54)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 23 and N(F) ≥ 55, using
- net from sequence [i] based on digital (23, 54)-sequence over F5, using
(27, 86, 299)-Net in Base 5 — Upper bound on s
There is no (27, 86, 300)-net in base 5, because
- 1 times m-reduction [i] would yield (27, 85, 300)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(585, 300, S5, 58), but
- the linear programming bound shows that M ≥ 634 525000 207082 536100 296561 804057 343269 503155 795860 421279 370751 410403 648468 789990 811511 209240 934546 557092 073293 393497 124270 652420 818805 694580 078125 / 1622 404032 421636 974309 186709 807435 620888 960222 026787 418196 121323 364094 426295 408276 101913 > 585 [i]
- extracting embedded orthogonal array [i] would yield OA(585, 300, S5, 58), but