Best Known (77−50, 77, s)-Nets in Base 16
(77−50, 77, 65)-Net over F16 — Constructive and digital
Digital (27, 77, 65)-net over F16, using
- t-expansion [i] based on digital (6, 77, 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
(77−50, 77, 120)-Net in Base 16 — Constructive
(27, 77, 120)-net in base 16, using
- 3 times m-reduction [i] based on (27, 80, 120)-net in base 16, using
- base change [i] based on digital (11, 64, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- base change [i] based on digital (11, 64, 120)-net over F32, using
(77−50, 77, 156)-Net over F16 — Digital
Digital (27, 77, 156)-net over F16, using
- net from sequence [i] based on digital (27, 155)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 27 and N(F) ≥ 156, using
(77−50, 77, 3455)-Net in Base 16 — Upper bound on s
There is no (27, 77, 3456)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 523 343701 490905 311266 081646 294059 033833 278553 103280 584468 263069 163375 848563 756254 686294 101001 > 1677 [i]