Best Known (105, 105+75, s)-Nets in Base 4
(105, 105+75, 130)-Net over F4 — Constructive and digital
Digital (105, 180, 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+75, 234)-Net over F4 — Digital
Digital (105, 180, 234)-net over F4, using
(105, 105+75, 3964)-Net in Base 4 — Upper bound on s
There is no (105, 180, 3965)-net in base 4, because
- 1 times m-reduction [i] would yield (105, 179, 3965)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 591367 319483 997065 385778 599031 416567 104587 636878 995645 702763 350062 571474 839307 288279 875951 902712 332531 197284 > 4179 [i]