Best Known (112, 112+74, s)-Nets in Base 4
(112, 112+74, 130)-Net over F4 — Constructive and digital
Digital (112, 186, 130)-net over F4, using
- t-expansion [i] based on digital (105, 186, 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
(112, 112+74, 279)-Net over F4 — Digital
Digital (112, 186, 279)-net over F4, using
(112, 112+74, 5162)-Net in Base 4 — Upper bound on s
There is no (112, 186, 5163)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 9683 876423 415808 218553 914221 826617 524287 952158 845624 513251 262982 335021 839440 806934 966511 827130 769240 430193 922188 > 4186 [i]