Best Known (117, 117+114, s)-Nets in Base 4
(117, 117+114, 130)-Net over F4 — Constructive and digital
Digital (117, 231, 130)-net over F4, using
- t-expansion [i] based on digital (105, 231, 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+114, 170)-Net over F4 — Digital
Digital (117, 231, 170)-net over F4, using
(117, 117+114, 1980)-Net in Base 4 — Upper bound on s
There is no (117, 231, 1981)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 12 190414 864162 647060 660255 584928 870390 674104 979188 570161 727840 229687 291366 813812 666232 376509 596211 687629 517139 498925 260220 860923 173083 762352 > 4231 [i]