Best Known (140−127, 140, s)-Nets in Base 9
(140−127, 140, 64)-Net over F9 — Constructive and digital
Digital (13, 140, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
(140−127, 140, 120)-Net in Base 9 — Upper bound on s
There is no (13, 140, 121)-net in base 9, because
- 34 times m-reduction [i] would yield (13, 106, 121)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9106, 121, S9, 93), but
- the linear programming bound shows that M ≥ 14386 856892 109753 589943 480991 392045 806312 525494 995317 258231 047340 377435 156302 384720 183485 695337 425818 836413 178517 / 99301 439965 > 9106 [i]
- extracting embedded orthogonal array [i] would yield OA(9106, 121, S9, 93), but