Best Known (71, 71+176, s)-Nets in Base 4
(71, 71+176, 66)-Net over F4 — Constructive and digital
Digital (71, 247, 66)-net over F4, using
- t-expansion [i] based on digital (49, 247, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 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) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
(71, 71+176, 105)-Net over F4 — Digital
Digital (71, 247, 105)-net over F4, using
- t-expansion [i] based on digital (70, 247, 105)-net over F4, using
- net from sequence [i] based on digital (70, 104)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 70 and N(F) ≥ 105, using
- net from sequence [i] based on digital (70, 104)-sequence over F4, using
(71, 71+176, 429)-Net over F4 — Upper bound on s (digital)
There is no digital (71, 247, 430)-net over F4, because
- extracting embedded orthogonal array [i] would yield linear OA(4247, 430, F4, 176) (dual of [430, 183, 177]-code), but
- residual code [i] would yield OA(471, 253, S4, 44), but
- the linear programming bound shows that M ≥ 27385 603782 383297 661406 789870 071468 501212 578772 565955 567440 744927 980401 898659 225594 231422 713856 / 4741 255951 754751 821637 567787 914724 985401 817073 767747 > 471 [i]
- residual code [i] would yield OA(471, 253, S4, 44), but
(71, 71+176, 478)-Net in Base 4 — Upper bound on s
There is no (71, 247, 479)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 57243 033892 319339 209774 415942 805419 430303 312667 292508 824913 705456 752308 327276 676371 647706 628476 644990 192568 796201 900252 341630 098970 329889 772594 754397 > 4247 [i]