Best Known (260−106, 260, s)-Nets in Base 4
(260−106, 260, 138)-Net over F4 — Constructive and digital
Digital (154, 260, 138)-net over F4, using
- t-expansion [i] based on digital (149, 260, 138)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (21, 76, 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, 184, 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, 76, 34)-net over F4, using
- (u, u+v)-construction [i] based on
(260−106, 260, 146)-Net in Base 4 — Constructive
(154, 260, 146)-net in base 4, using
- t-expansion [i] based on (153, 260, 146)-net in base 4, using
- (u, u+v)-construction [i] based on
- (27, 80, 42)-net in base 4, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- digital (73, 180, 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
- (27, 80, 42)-net in base 4, using
- (u, u+v)-construction [i] based on
(260−106, 260, 347)-Net over F4 — Digital
Digital (154, 260, 347)-net over F4, using
(260−106, 260, 6124)-Net in Base 4 — Upper bound on s
There is no (154, 260, 6125)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3 437175 804035 514979 602379 270676 010412 804709 440395 357618 788160 364012 887141 250660 124222 605201 447192 846956 943668 423530 258276 483282 457639 246847 318061 911130 269936 > 4260 [i]