Best Known (36, 36+51, s)-Nets in Base 64
(36, 36+51, 513)-Net over F64 — Constructive and digital
Digital (36, 87, 513)-net over F64, using
- t-expansion [i] based on digital (28, 87, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(36, 36+51, 263951)-Net in Base 64 — Upper bound on s
There is no (36, 87, 263952)-net in base 64, because
- 1 times m-reduction [i] would yield (36, 86, 263952)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 214536 848342 068314 986605 095669 752241 292669 125588 745095 677807 084605 276380 856169 469381 859175 960102 229753 694012 620322 368166 459560 255503 347577 700201 950682 913168 > 6486 [i]