Best Known (9, 9+30, s)-Nets in Base 5
(9, 9+30, 26)-Net over F5 — Constructive and digital
Digital (9, 39, 26)-net over F5, using
- net from sequence [i] based on digital (9, 25)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 9 and N(F) ≥ 26, using
(9, 9+30, 87)-Net over F5 — Upper bound on s (digital)
There is no digital (9, 39, 88)-net over F5, because
- extracting embedded orthogonal array [i] would yield linear OA(539, 88, F5, 30) (dual of [88, 49, 31]-code), but
- residual code [i] would yield OA(59, 57, S5, 6), but
- the linear programming bound shows that M ≥ 89349 609375 / 43961 > 59 [i]
- residual code [i] would yield OA(59, 57, S5, 6), but
(9, 9+30, 88)-Net in Base 5 — Upper bound on s
There is no (9, 39, 89)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(539, 89, S5, 30), but
- the linear programming bound shows that M ≥ 10 998634 290952 091743 995634 814347 972284 312017 959290 863621 195385 348983 108997 344970 703125 / 5975 658837 839706 727949 697506 172731 600224 929862 381411 729681 > 539 [i]