Best Known (232−110, 232, s)-Nets in Base 4
(232−110, 232, 130)-Net over F4 — Constructive and digital
Digital (122, 232, 130)-net over F4, using
- t-expansion [i] based on digital (105, 232, 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
(232−110, 232, 194)-Net over F4 — Digital
Digital (122, 232, 194)-net over F4, using
(232−110, 232, 2418)-Net in Base 4 — Upper bound on s
There is no (122, 232, 2419)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 47 686616 889295 011171 231410 967122 249768 686665 254789 530148 230650 235328 795378 438698 605885 783258 438946 447550 396306 773221 597329 021499 127790 296960 > 4232 [i]