Best Known (42, 101, s)-Nets in Base 4
(42, 101, 56)-Net over F4 — Constructive and digital
Digital (42, 101, 56)-net over F4, using
- t-expansion [i] based on digital (33, 101, 56)-net over F4, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 from the 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) = 33 and N(F) ≥ 56, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
(42, 101, 75)-Net over F4 — Digital
Digital (42, 101, 75)-net over F4, using
- t-expansion [i] based on digital (40, 101, 75)-net over F4, using
- net from sequence [i] based on digital (40, 74)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 40 and N(F) ≥ 75, using
- net from sequence [i] based on digital (40, 74)-sequence over F4, using
(42, 101, 440)-Net in Base 4 — Upper bound on s
There is no (42, 101, 441)-net in base 4, because
- 1 times m-reduction [i] would yield (42, 100, 441)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 1 678113 656539 053610 154450 357229 449048 060683 111689 959383 113280 > 4100 [i]