Best Known (35, 35+71, s)-Nets in Base 4
(35, 35+71, 56)-Net over F4 — Constructive and digital
Digital (35, 106, 56)-net over F4, using
- t-expansion [i] based on digital (33, 106, 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
(35, 35+71, 65)-Net over F4 — Digital
Digital (35, 106, 65)-net over F4, using
- t-expansion [i] based on digital (33, 106, 65)-net over F4, using
- net from sequence [i] based on digital (33, 64)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 65, using
- net from sequence [i] based on digital (33, 64)-sequence over F4, using
(35, 35+71, 269)-Net in Base 4 — Upper bound on s
There is no (35, 106, 270)-net in base 4, because
- 1 times m-reduction [i] would yield (35, 105, 270)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 1841 115579 484124 042805 755204 220567 061304 788424 427562 296685 921840 > 4105 [i]