Best Known (105, 105+97, s)-Nets in Base 4
(105, 105+97, 130)-Net over F4 — Constructive and digital
Digital (105, 202, 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+97, 165)-Net over F4 — Digital
Digital (105, 202, 165)-net over F4, using
(105, 105+97, 2034)-Net in Base 4 — Upper bound on s
There is no (105, 202, 2035)-net in base 4, because
- 1 times m-reduction [i] would yield (105, 201, 2035)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 10 396617 534528 728851 077671 131836 181139 550242 015337 059983 782100 400447 729401 666068 165896 941327 155933 567954 709575 491069 326783 > 4201 [i]