Best Known (82−44, 82, s)-Nets in Base 81
(82−44, 82, 730)-Net over F81 — Constructive and digital
Digital (38, 82, 730)-net over F81, using
- t-expansion [i] based on digital (36, 82, 730)-net over F81, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- the Hermitian function field over F81 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
(82−44, 82, 942)-Net over F81 — Digital
Digital (38, 82, 942)-net over F81, using
(82−44, 82, 1469616)-Net in Base 81 — Upper bound on s
There is no (38, 82, 1469617)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3 131661 757464 064489 555032 203011 930346 835283 196863 536413 989311 356925 144227 761522 964084 445967 322133 291021 424087 300887 446980 504578 872027 648886 808748 592577 841121 > 8182 [i]