Best Known (106, 106+79, s)-Nets in Base 4
(106, 106+79, 130)-Net over F4 — Constructive and digital
Digital (106, 185, 130)-net over F4, using
- t-expansion [i] based on digital (105, 185, 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
(106, 106+79, 221)-Net over F4 — Digital
Digital (106, 185, 221)-net over F4, using
(106, 106+79, 3522)-Net in Base 4 — Upper bound on s
There is no (106, 185, 3523)-net in base 4, because
- 1 times m-reduction [i] would yield (106, 184, 3523)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 603 065812 223069 599254 567372 142823 628822 999216 186867 446879 917129 893135 693531 241362 923010 657200 465113 212567 612544 > 4184 [i]