Best Known (121, 121+121, s)-Nets in Base 4
(121, 121+121, 130)-Net over F4 — Constructive and digital
Digital (121, 242, 130)-net over F4, using
- t-expansion [i] based on digital (105, 242, 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
(121, 121+121, 170)-Net over F4 — Digital
Digital (121, 242, 170)-net over F4, using
(121, 121+121, 1976)-Net in Base 4 — Upper bound on s
There is no (121, 242, 1977)-net in base 4, because
- 1 times m-reduction [i] would yield (121, 241, 1977)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 12 765254 130210 089883 107929 705717 345293 796327 040115 625770 129508 385605 590498 151494 548840 184276 501968 824749 826017 743742 150824 927105 183058 883658 442976 > 4241 [i]