Best Known (134, 134+110, s)-Nets in Base 4
(134, 134+110, 130)-Net over F4 — Constructive and digital
Digital (134, 244, 130)-net over F4, using
- t-expansion [i] based on digital (105, 244, 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
(134, 134+110, 237)-Net over F4 — Digital
Digital (134, 244, 237)-net over F4, using
(134, 134+110, 3289)-Net in Base 4 — Upper bound on s
There is no (134, 244, 3290)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 810 907279 019184 277523 845558 894190 088384 715048 599475 274890 144425 077627 823649 880134 268673 386497 572786 625582 342481 278888 290993 869376 377704 297525 134520 > 4244 [i]