Best Known (128, 128+112, s)-Nets in Base 4
(128, 128+112, 130)-Net over F4 — Constructive and digital
Digital (128, 240, 130)-net over F4, using
- t-expansion [i] based on digital (105, 240, 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, 128+112, 210)-Net over F4 — Digital
Digital (128, 240, 210)-net over F4, using
(128, 128+112, 2706)-Net in Base 4 — Upper bound on s
There is no (128, 240, 2707)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3 125716 879119 265196 147523 252891 265662 348902 532731 983914 492457 325205 381549 785611 684698 946742 544532 402073 104641 728334 439205 771195 550935 108926 760560 > 4240 [i]