Best Known (216−106, 216, s)-Nets in Base 4
(216−106, 216, 130)-Net over F4 — Constructive and digital
Digital (110, 216, 130)-net over F4, using
- t-expansion [i] based on digital (105, 216, 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
(216−106, 216, 165)-Net over F4 — Digital
Digital (110, 216, 165)-net over F4, using
- t-expansion [i] based on digital (109, 216, 165)-net over F4, using
- net from sequence [i] based on digital (109, 164)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 109 and N(F) ≥ 165, using
- net from sequence [i] based on digital (109, 164)-sequence over F4, using
(216−106, 216, 1908)-Net in Base 4 — Upper bound on s
There is no (110, 216, 1909)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 11361 613744 237008 651166 260840 262368 346576 391249 287480 527672 476930 778207 780706 000975 193318 346538 663159 131282 708433 563570 505687 785340 > 4216 [i]