Best Known (25, 25+55, s)-Nets in Base 4
(25, 25+55, 34)-Net over F4 — Constructive and digital
Digital (25, 80, 34)-net over F4, using
- t-expansion [i] based on digital (21, 80, 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
(25, 25+55, 35)-Net in Base 4 — Constructive
(25, 80, 35)-net in base 4, using
- t-expansion [i] based on (24, 80, 35)-net in base 4, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
- base expansion [i] based on digital (48, 34)-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 2 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]
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
(25, 25+55, 51)-Net over F4 — Digital
Digital (25, 80, 51)-net over F4, using
- net from sequence [i] based on digital (25, 50)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 25 and N(F) ≥ 51, using
(25, 25+55, 189)-Net in Base 4 — Upper bound on s
There is no (25, 80, 190)-net in base 4, because
- 1 times m-reduction [i] would yield (25, 79, 190)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 407298 841968 003846 786250 457382 060396 052936 860910 > 479 [i]