Best Known (106, 106+75, s)-Nets in Base 4
(106, 106+75, 130)-Net over F4 — Constructive and digital
Digital (106, 181, 130)-net over F4, using
- t-expansion [i] based on digital (105, 181, 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+75, 239)-Net over F4 — Digital
Digital (106, 181, 239)-net over F4, using
(106, 106+75, 4116)-Net in Base 4 — Upper bound on s
There is no (106, 181, 4117)-net in base 4, because
- 1 times m-reduction [i] would yield (106, 180, 4117)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2 354354 817796 941006 317507 133211 835956 096035 152982 511856 003343 798233 533157 361238 532589 102036 535989 832015 045120 > 4180 [i]