Best Known (105, 105+103, s)-Nets in Base 4
(105, 105+103, 130)-Net over F4 — Constructive and digital
Digital (105, 208, 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
(105, 105+103, 153)-Net over F4 — Digital
Digital (105, 208, 153)-net over F4, using
(105, 105+103, 1796)-Net in Base 4 — Upper bound on s
There is no (105, 208, 1797)-net in base 4, because
- 1 times m-reduction [i] would yield (105, 207, 1797)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 42838 955466 342708 379620 293404 859167 332787 064740 904978 136733 226490 860366 333769 606763 487481 132448 411218 460864 283767 575079 238080 > 4207 [i]