Best Known (122, 122+118, s)-Nets in Base 4
(122, 122+118, 130)-Net over F4 — Constructive and digital
Digital (122, 240, 130)-net over F4, using
- t-expansion [i] based on digital (105, 240, 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+118, 178)-Net over F4 — Digital
Digital (122, 240, 178)-net over F4, using
(122, 122+118, 2091)-Net in Base 4 — Upper bound on s
There is no (122, 240, 2092)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3 202737 657501 324097 774818 395305 619693 100129 536628 997805 910227 954229 127821 805738 118449 209838 195684 412302 129902 448601 068730 570305 200996 828335 747200 > 4240 [i]