Best Known (122, 122+91, s)-Nets in Base 4
(122, 122+91, 130)-Net over F4 — Constructive and digital
Digital (122, 213, 130)-net over F4, using
- t-expansion [i] based on digital (105, 213, 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+91, 250)-Net over F4 — Digital
Digital (122, 213, 250)-net over F4, using
(122, 122+91, 3994)-Net in Base 4 — Upper bound on s
There is no (122, 213, 3995)-net in base 4, because
- 1 times m-reduction [i] would yield (122, 212, 3995)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 43 695922 180070 539442 271593 642102 787371 361793 970711 504686 311291 967115 918835 094252 288713 135534 787005 486304 811593 129137 753501 561184 > 4212 [i]