Best Known (106, 106+110, s)-Nets in Base 4
(106, 106+110, 130)-Net over F4 — Constructive and digital
Digital (106, 216, 130)-net over F4, using
- t-expansion [i] based on digital (105, 216, 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
(106, 106+110, 145)-Net over F4 — Digital
Digital (106, 216, 145)-net over F4, using
(106, 106+110, 1601)-Net in Base 4 — Upper bound on s
There is no (106, 216, 1602)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 11327 913000 251695 207748 105624 294009 099856 942239 546910 028011 635039 327533 091577 728861 162106 568929 004706 260632 258494 333523 310528 154464 > 4216 [i]