Best Known (133, 133+112, s)-Nets in Base 4
(133, 133+112, 130)-Net over F4 — Constructive and digital
Digital (133, 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
(133, 133+112, 228)-Net over F4 — Digital
Digital (133, 245, 228)-net over F4, using
(133, 133+112, 3069)-Net in Base 4 — Upper bound on s
There is no (133, 245, 3070)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3218 504391 224156 815215 452911 848723 382275 690863 648156 715961 971119 352720 393685 895271 260425 711602 778319 322493 988642 073131 805473 087706 663576 362647 783669 > 4245 [i]