Best Known (35, 35+44, s)-Nets in Base 64
(35, 35+44, 513)-Net over F64 — Constructive and digital
Digital (35, 79, 513)-net over F64, using
- t-expansion [i] based on digital (28, 79, 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
(35, 35+44, 575)-Net over F64 — Digital
Digital (35, 79, 575)-net over F64, using
(35, 35+44, 439875)-Net in Base 64 — Upper bound on s
There is no (35, 79, 439876)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 48778 340705 312005 053303 789916 802557 843417 824779 669831 199314 523240 593513 185420 359279 786156 577286 787050 420082 504119 858435 931322 595722 417721 510896 > 6479 [i]