Best Known (122, 122+95, s)-Nets in Base 4
(122, 122+95, 130)-Net over F4 — Constructive and digital
Digital (122, 217, 130)-net over F4, using
- t-expansion [i] based on digital (105, 217, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(122, 122+95, 235)-Net over F4 — Digital
Digital (122, 217, 235)-net over F4, using
(122, 122+95, 3541)-Net in Base 4 — Upper bound on s
There is no (122, 217, 3542)-net in base 4, because
- 1 times m-reduction [i] would yield (122, 216, 3542)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 11153 939318 219984 372331 390705 154494 667652 186146 727910 990667 995649 233813 761041 246356 288147 238101 490135 500580 018349 310648 866028 203920 > 4216 [i]