Best Known (47, 47+87, s)-Nets in Base 4
(47, 47+87, 56)-Net over F4 — Constructive and digital
Digital (47, 134, 56)-net over F4, using
- t-expansion [i] based on digital (33, 134, 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
(47, 47+87, 81)-Net over F4 — Digital
Digital (47, 134, 81)-net over F4, using
- t-expansion [i] based on digital (46, 134, 81)-net over F4, using
- net from sequence [i] based on digital (46, 80)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 46 and N(F) ≥ 81, using
- net from sequence [i] based on digital (46, 80)-sequence over F4, using
(47, 47+87, 375)-Net in Base 4 — Upper bound on s
There is no (47, 134, 376)-net in base 4, because
- 1 times m-reduction [i] would yield (47, 133, 376)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 124 359419 996280 088253 202547 977766 834573 296341 021968 895832 479761 565075 486079 858034 > 4133 [i]