Best Known (122, 122+101, s)-Nets in Base 4
(122, 122+101, 130)-Net over F4 — Constructive and digital
Digital (122, 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
(122, 122+101, 216)-Net over F4 — Digital
Digital (122, 223, 216)-net over F4, using
(122, 122+101, 3018)-Net in Base 4 — Upper bound on s
There is no (122, 223, 3019)-net in base 4, because
- 1 times m-reduction [i] would yield (122, 222, 3019)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 45 577308 658580 495484 478429 009789 240660 475374 614138 027393 149090 894683 827997 618732 030887 511839 572879 077679 039384 756344 612209 484433 156476 > 4222 [i]