Best Known (44, 44+80, s)-Nets in Base 4
(44, 44+80, 56)-Net over F4 — Constructive and digital
Digital (44, 124, 56)-net over F4, using
- t-expansion [i] based on digital (33, 124, 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
(44, 44+80, 75)-Net over F4 — Digital
Digital (44, 124, 75)-net over F4, using
- t-expansion [i] based on digital (40, 124, 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
(44, 44+80, 354)-Net in Base 4 — Upper bound on s
There is no (44, 124, 355)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 471 108207 930319 319905 038985 715202 440280 097806 671627 601324 201216 341754 633064 > 4124 [i]