Best Known (116, 116+106, s)-Nets in Base 4
(116, 116+106, 130)-Net over F4 — Constructive and digital
Digital (116, 222, 130)-net over F4, using
- t-expansion [i] based on digital (105, 222, 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
(116, 116+106, 182)-Net over F4 — Digital
Digital (116, 222, 182)-net over F4, using
(116, 116+106, 2239)-Net in Base 4 — Upper bound on s
There is no (116, 222, 2240)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 45 798241 457272 971860 543088 372971 633832 264854 406991 790106 437206 302348 817492 389225 427075 669883 215969 158081 879629 991260 959023 975790 102051 > 4222 [i]