Best Known (170−64, 170, s)-Nets in Base 4
(170−64, 170, 130)-Net over F4 — Constructive and digital
Digital (106, 170, 130)-net over F4, using
- t-expansion [i] based on digital (105, 170, 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
(170−64, 170, 312)-Net over F4 — Digital
Digital (106, 170, 312)-net over F4, using
(170−64, 170, 6706)-Net in Base 4 — Upper bound on s
There is no (106, 170, 6707)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2 242061 898814 977978 893389 991066 786461 379015 595978 327740 926846 515770 294742 619173 775326 906863 684050 136335 > 4170 [i]