Best Known (122, 122+106, s)-Nets in Base 4
(122, 122+106, 130)-Net over F4 — Constructive and digital
Digital (122, 228, 130)-net over F4, using
- t-expansion [i] based on digital (105, 228, 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+106, 203)-Net over F4 — Digital
Digital (122, 228, 203)-net over F4, using
(122, 122+106, 2627)-Net in Base 4 — Upper bound on s
There is no (122, 228, 2628)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 187771 920308 140531 455254 272646 141333 612456 534999 704558 328883 614827 168231 801202 763754 001584 635229 958474 072451 849431 877533 714196 560682 277360 > 4228 [i]