Best Known (215−90, 215, s)-Nets in Base 4
(215−90, 215, 130)-Net over F4 — Constructive and digital
Digital (125, 215, 130)-net over F4, using
- t-expansion [i] based on digital (105, 215, 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
(215−90, 215, 269)-Net over F4 — Digital
Digital (125, 215, 269)-net over F4, using
(215−90, 215, 4384)-Net in Base 4 — Upper bound on s
There is no (125, 215, 4385)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2785 903797 311036 686328 134899 062041 085521 989677 428467 768664 951827 810596 081160 426642 658733 983033 994144 087914 325172 441860 051369 476096 > 4215 [i]