Best Known (133, 133+122, s)-Nets in Base 4
(133, 133+122, 130)-Net over F4 — Constructive and digital
Digital (133, 255, 130)-net over F4, using
- t-expansion [i] based on digital (105, 255, 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
(133, 133+122, 205)-Net over F4 — Digital
Digital (133, 255, 205)-net over F4, using
(133, 133+122, 2531)-Net in Base 4 — Upper bound on s
There is no (133, 255, 2532)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3371 589866 701951 075581 988204 362209 289209 207428 978326 736460 606898 505833 314441 636693 729199 964073 508467 042788 936727 673346 349672 335072 444757 285146 828119 841360 > 4255 [i]