Best Known (10, 10+30, s)-Nets in Base 5
(10, 10+30, 26)-Net over F5 — Constructive and digital
Digital (10, 40, 26)-net over F5, using
- t-expansion [i] based on digital (9, 40, 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
- net from sequence [i] based on digital (9, 25)-sequence over F5, using
(10, 10+30, 27)-Net over F5 — Digital
Digital (10, 40, 27)-net over F5, using
- net from sequence [i] based on digital (10, 26)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 10 and N(F) ≥ 27, using
(10, 10+30, 106)-Net in Base 5 — Upper bound on s
There is no (10, 40, 107)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 9114 229293 184050 457118 705845 > 540 [i]
- extracting embedded orthogonal array [i] would yield OA(540, 107, S5, 30), but
- the linear programming bound shows that M ≥ 2 444583 551382 201850 781520 395853 708391 699789 897762 821055 948734 283447 265625 / 251 181963 463860 852519 484964 340757 927650 764452 > 540 [i]