Best Known (86, 86+44, s)-Nets in Base 2
(86, 86+44, 68)-Net over F2 — Constructive and digital
Digital (86, 130, 68)-net over F2, using
- trace code for nets [i] based on digital (21, 65, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
(86, 86+44, 95)-Net over F2 — Digital
Digital (86, 130, 95)-net over F2, using
(86, 86+44, 512)-Net in Base 2 — Upper bound on s
There is no (86, 130, 513)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1392 250576 663000 496546 555994 545074 546432 > 2130 [i]