Best Known (65−55, 65, s)-Nets in Base 9
(65−55, 65, 40)-Net over F9 — Constructive and digital
Digital (10, 65, 40)-net over F9, using
- t-expansion [i] based on digital (8, 65, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
(65−55, 65, 54)-Net over F9 — Digital
Digital (10, 65, 54)-net over F9, using
- net from sequence [i] based on digital (10, 53)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 10 and N(F) ≥ 54, using
(65−55, 65, 196)-Net in Base 9 — Upper bound on s
There is no (10, 65, 197)-net in base 9, because
- 2 times m-reduction [i] would yield (10, 63, 197)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(963, 197, S9, 53), but
- the linear programming bound shows that M ≥ 127169 296363 566212 434644 789290 032451 398813 361778 136520 150124 453239 912036 588555 431675 332274 184206 274202 994825 807187 253105 417946 662922 857900 023040 / 91555 015747 473642 311727 358029 235533 442026 392623 556556 037801 707642 946307 663056 919393 > 963 [i]
- extracting embedded orthogonal array [i] would yield OA(963, 197, S9, 53), but