Best Known (36−31, 36, s)-Nets in Base 64
(36−31, 36, 128)-Net over F64 — Constructive and digital
Digital (5, 36, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
(36−31, 36, 133)-Net over F64 — Digital
Digital (5, 36, 133)-net over F64, using
- net from sequence [i] based on digital (5, 132)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 133, using
(36−31, 36, 1663)-Net in Base 64 — Upper bound on s
There is no (5, 36, 1664)-net in base 64, because
- 1 times m-reduction [i] would yield (5, 35, 1664)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 1656 371781 558769 726669 247816 828992 580916 011081 512976 444083 441585 > 6435 [i]