Best Known (79, 79+46, s)-Nets in Base 4
(79, 79+46, 130)-Net over F4 — Constructive and digital
Digital (79, 125, 130)-net over F4, using
- 21 times m-reduction [i] based on digital (79, 146, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 73, 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
- trace code for nets [i] based on digital (6, 73, 65)-net over F16, using
(79, 79+46, 260)-Net over F4 — Digital
Digital (79, 125, 260)-net over F4, using
(79, 79+46, 5861)-Net in Base 4 — Upper bound on s
There is no (79, 125, 5862)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1811 617930 845672 637295 704083 193260 609738 745071 789645 198556 473579 728252 599408 > 4125 [i]