Best Known (89−77, 89, s)-Nets in Base 32
(89−77, 89, 120)-Net over F32 — Constructive and digital
Digital (12, 89, 120)-net over F32, using
- t-expansion [i] based on digital (11, 89, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
(89−77, 89, 129)-Net over F32 — Digital
Digital (12, 89, 129)-net over F32, using
- net from sequence [i] based on digital (12, 128)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 12 and N(F) ≥ 129, using
(89−77, 89, 1463)-Net in Base 32 — Upper bound on s
There is no (12, 89, 1464)-net in base 32, because
- 1 times m-reduction [i] would yield (12, 88, 1464)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2 910970 832116 370591 175639 570166 391654 943935 108025 538279 953027 170079 951305 057700 712557 560783 182471 537224 503807 610504 913410 997122 869665 > 3288 [i]