Best Known (65−39, 65, s)-Nets in Base 4
(65−39, 65, 34)-Net over F4 — Constructive and digital
Digital (26, 65, 34)-net over F4, using
- t-expansion [i] based on digital (21, 65, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second 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) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
(65−39, 65, 36)-Net in Base 4 — Constructive
(26, 65, 36)-net in base 4, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 3 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
(65−39, 65, 55)-Net over F4 — Digital
Digital (26, 65, 55)-net over F4, using
- net from sequence [i] based on digital (26, 54)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 26 and N(F) ≥ 55, using
(65−39, 65, 266)-Net in Base 4 — Upper bound on s
There is no (26, 65, 267)-net in base 4, because
- 1 times m-reduction [i] would yield (26, 64, 267)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 343 167359 651330 163731 776810 333664 193088 > 464 [i]