Best Known (100−64, 100, s)-Nets in Base 4
(100−64, 100, 56)-Net over F4 — Constructive and digital
Digital (36, 100, 56)-net over F4, using
- t-expansion [i] based on digital (33, 100, 56)-net over F4, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 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) = 33 and N(F) ≥ 56, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
(100−64, 100, 65)-Net over F4 — Digital
Digital (36, 100, 65)-net over F4, using
- t-expansion [i] based on digital (33, 100, 65)-net over F4, using
- net from sequence [i] based on digital (33, 64)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 65, using
- net from sequence [i] based on digital (33, 64)-sequence over F4, using
(100−64, 100, 298)-Net in Base 4 — Upper bound on s
There is no (36, 100, 299)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(4100, 299, S4, 64), but
- 1 times code embedding in larger space [i] would yield OA(4101, 300, S4, 64), but
- the linear programming bound shows that M ≥ 1 231265 431537 788363 998593 064935 723340 754119 840201 132340 137144 126545 911415 806525 100699 435502 000219 063131 921131 435910 945455 478688 417027 331901 674121 045545 301803 617922 641716 838400 / 170245 555311 187291 018741 043496 578809 211994 161262 146673 891958 873123 481881 751387 033606 486355 185045 431953 178363 079839 > 4101 [i]
- 1 times code embedding in larger space [i] would yield OA(4101, 300, S4, 64), but