Best Known (69, 138, s)-Nets in Base 9
(69, 138, 165)-Net over F9 — Constructive and digital
Digital (69, 138, 165)-net over F9, using
- t-expansion [i] based on digital (64, 138, 165)-net over F9, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
(69, 138, 258)-Net over F9 — Digital
Digital (69, 138, 258)-net over F9, using
(69, 138, 11821)-Net in Base 9 — Upper bound on s
There is no (69, 138, 11822)-net in base 9, because
- 1 times m-reduction [i] would yield (69, 137, 11822)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 53984 449779 128591 637080 922532 177898 422705 881946 302763 228469 398436 610907 072969 370257 577459 024366 901674 006485 980834 654294 344449 788705 > 9137 [i]