Best Known (122, 245, s)-Nets in Base 4
(122, 245, 130)-Net over F4 — Constructive and digital
Digital (122, 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
(122, 245, 170)-Net over F4 — Digital
Digital (122, 245, 170)-net over F4, using
(122, 245, 1960)-Net in Base 4 — Upper bound on s
There is no (122, 245, 1961)-net in base 4, because
- 1 times m-reduction [i] would yield (122, 244, 1961)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 803 822829 351304 228172 012384 376459 454333 516152 651853 024425 012460 681621 209543 142544 815488 346524 266079 128152 201823 632933 869841 775793 401703 077173 292800 > 4244 [i]