Best Known (30, 30+32, s)-Nets in Base 16
(30, 30+32, 130)-Net over F16 — Constructive and digital
Digital (30, 62, 130)-net over F16, using
- 4 times m-reduction [i] based on digital (30, 66, 130)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 24, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- digital (6, 42, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16 (see above)
- digital (6, 24, 65)-net over F16, using
- (u, u+v)-construction [i] based on
(30, 30+32, 192)-Net in Base 16 — Constructive
(30, 62, 192)-net in base 16, using
- 1 times m-reduction [i] based on (30, 63, 192)-net in base 16, using
- base change [i] based on digital (3, 36, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 36, 192)-net over F128, using
(30, 30+32, 213)-Net over F16 — Digital
Digital (30, 62, 213)-net over F16, using
(30, 30+32, 21000)-Net in Base 16 — Upper bound on s
There is no (30, 62, 21001)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 452 390804 520647 507981 965052 895722 485424 638546 943792 673498 827944 256495 091616 > 1662 [i]