Best Known (128, 245, s)-Nets in Base 4
(128, 245, 130)-Net over F4 — Constructive and digital
Digital (128, 245, 130)-net over F4, using
- t-expansion [i] based on digital (105, 245, 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
(128, 245, 199)-Net over F4 — Digital
Digital (128, 245, 199)-net over F4, using
(128, 245, 2504)-Net in Base 4 — Upper bound on s
There is no (128, 245, 2505)-net in base 4, because
- 1 times m-reduction [i] would yield (128, 244, 2505)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 805 037482 182556 954617 060585 348263 920009 293422 127207 899468 748392 127981 729217 988029 753016 017736 569675 126015 888279 292562 719482 132810 621151 709035 408224 > 4244 [i]