Best Known (38, 38+74, s)-Nets in Base 4
(38, 38+74, 56)-Net over F4 — Constructive and digital
Digital (38, 112, 56)-net over F4, using
- t-expansion [i] based on digital (33, 112, 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
(38, 38+74, 66)-Net over F4 — Digital
Digital (38, 112, 66)-net over F4, using
- t-expansion [i] based on digital (37, 112, 66)-net over F4, using
- net from sequence [i] based on digital (37, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 37 and N(F) ≥ 66, using
- net from sequence [i] based on digital (37, 65)-sequence over F4, using
(38, 38+74, 295)-Net in Base 4 — Upper bound on s
There is no (38, 112, 296)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 29 455829 335225 016100 677390 449684 654893 973650 444169 695541 082022 156547 > 4112 [i]