Best Known (145, 237, s)-Nets in Base 4
(145, 237, 138)-Net over F4 — Constructive and digital
Digital (145, 237, 138)-net over F4, using
- 10 times m-reduction [i] based on digital (145, 247, 138)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (21, 72, 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
- digital (73, 175, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 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) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- digital (21, 72, 34)-net over F4, using
- (u, u+v)-construction [i] based on
(145, 237, 140)-Net in Base 4 — Constructive
(145, 237, 140)-net in base 4, using
- (u, u+v)-construction [i] based on
- (26, 72, 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
- net from sequence [i] based on (26, 35)-sequence in base 4, using
- digital (73, 165, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 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) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- (26, 72, 36)-net in base 4, using
(145, 237, 375)-Net over F4 — Digital
Digital (145, 237, 375)-net over F4, using
(145, 237, 7548)-Net in Base 4 — Upper bound on s
There is no (145, 237, 7549)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 48933 164389 784804 096245 901330 844274 953076 274544 346721 832002 696862 744078 309524 266715 281263 615594 283843 946064 534349 623900 349607 456726 820190 070056 > 4237 [i]