Best Known (126, 126+119, s)-Nets in Base 4
(126, 126+119, 130)-Net over F4 — Constructive and digital
Digital (126, 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
(126, 126+119, 188)-Net over F4 — Digital
Digital (126, 245, 188)-net over F4, using
(126, 126+119, 2301)-Net in Base 4 — Upper bound on s
There is no (126, 245, 2302)-net in base 4, because
- 1 times m-reduction [i] would yield (126, 244, 2302)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 802 138158 781218 242630 966276 949106 177251 730538 977999 456571 927031 613786 734680 837180 307128 848860 613624 739170 829271 160561 068871 419479 184399 554467 529878 > 4244 [i]