Best Known (245−121, 245, s)-Nets in Base 4
(245−121, 245, 130)-Net over F4 — Constructive and digital
Digital (124, 245, 130)-net over F4, using
- t-expansion [i] based on digital (105, 245, 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
(245−121, 245, 179)-Net over F4 — Digital
Digital (124, 245, 179)-net over F4, using
(245−121, 245, 2121)-Net in Base 4 — Upper bound on s
There is no (124, 245, 2122)-net in base 4, because
- 1 times m-reduction [i] would yield (124, 244, 2122)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 808 306801 528944 052598 979355 290863 673134 137214 084990 423957 040351 915991 460163 072080 399856 741406 646526 635556 975382 629801 991461 589956 640359 607046 222416 > 4244 [i]