Best Known (122, 239, s)-Nets in Base 4
(122, 239, 130)-Net over F4 — Constructive and digital
Digital (122, 239, 130)-net over F4, using
- t-expansion [i] based on digital (105, 239, 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, 239, 180)-Net over F4 — Digital
Digital (122, 239, 180)-net over F4, using
(122, 239, 2163)-Net in Base 4 — Upper bound on s
There is no (122, 239, 2164)-net in base 4, because
- 1 times m-reduction [i] would yield (122, 238, 2164)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 196357 332113 940191 800453 854106 558044 605341 463117 696551 052908 470596 603473 253320 315438 397822 627344 399597 214570 935547 736688 302118 028688 394791 175240 > 4238 [i]