Best Known (135−67, 135, s)-Nets in Base 9
(135−67, 135, 165)-Net over F9 — Constructive and digital
Digital (68, 135, 165)-net over F9, using
- t-expansion [i] based on digital (64, 135, 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
(135−67, 135, 261)-Net over F9 — Digital
Digital (68, 135, 261)-net over F9, using
(135−67, 135, 12312)-Net in Base 9 — Upper bound on s
There is no (68, 135, 12313)-net in base 9, because
- 1 times m-reduction [i] would yield (68, 134, 12313)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 73 907075 958095 475336 364308 250887 193487 031545 169555 318233 553050 232591 659532 613595 442219 395189 731969 857087 987096 081335 420458 094025 > 9134 [i]