Best Known (117, 117+106, s)-Nets in Base 4
(117, 117+106, 130)-Net over F4 — Constructive and digital
Digital (117, 223, 130)-net over F4, using
- t-expansion [i] based on digital (105, 223, 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
(117, 117+106, 186)-Net over F4 — Digital
Digital (117, 223, 186)-net over F4, using
(117, 117+106, 2300)-Net in Base 4 — Upper bound on s
There is no (117, 223, 2301)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 185 257897 519093 249883 223019 294058 091369 651717 916224 393355 345577 215187 216754 307471 930216 814832 537228 863575 523247 998193 995829 975070 790692 > 4223 [i]