Best Known (122, 122+82, s)-Nets in Base 4
(122, 122+82, 130)-Net over F4 — Constructive and digital
Digital (122, 204, 130)-net over F4, using
- t-expansion [i] based on digital (105, 204, 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+82, 293)-Net over F4 — Digital
Digital (122, 204, 293)-net over F4, using
(122, 122+82, 5292)-Net in Base 4 — Upper bound on s
There is no (122, 204, 5293)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 663 662267 609947 602937 246686 256724 924874 825458 419722 399023 381426 354543 553557 927537 826765 996871 087653 777039 490763 570899 435120 > 4204 [i]