Best Known (257−122, 257, s)-Nets in Base 4
(257−122, 257, 130)-Net over F4 — Constructive and digital
Digital (135, 257, 130)-net over F4, using
- t-expansion [i] based on digital (105, 257, 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
(257−122, 257, 211)-Net over F4 — Digital
Digital (135, 257, 211)-net over F4, using
(257−122, 257, 2651)-Net in Base 4 — Upper bound on s
There is no (135, 257, 2652)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 53887 431451 326572 872828 239169 018237 703621 945828 846506 932976 774276 807846 831113 610063 739636 584036 930774 923394 756271 539011 442840 389194 664087 037520 913130 540720 > 4257 [i]