Best Known (232−101, 232, s)-Nets in Base 4
(232−101, 232, 130)-Net over F4 — Constructive and digital
Digital (131, 232, 130)-net over F4, using
- t-expansion [i] based on digital (105, 232, 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
(232−101, 232, 254)-Net over F4 — Digital
Digital (131, 232, 254)-net over F4, using
(232−101, 232, 3885)-Net in Base 4 — Upper bound on s
There is no (131, 232, 3886)-net in base 4, because
- 1 times m-reduction [i] would yield (131, 231, 3886)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 11 913693 759041 277212 204479 495092 362000 302775 254748 904489 429905 569748 325562 735964 441005 972890 970607 372107 935177 154329 352372 040143 622128 898656 > 4231 [i]