Best Known (115, 115+73, s)-Nets in Base 2
(115, 115+73, 68)-Net over F2 — Constructive and digital
Digital (115, 188, 68)-net over F2, using
- trace code for nets [i] based on digital (21, 94, 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
(115, 115+73, 94)-Net over F2 — Digital
Digital (115, 188, 94)-net over F2, using
(115, 115+73, 471)-Net in Base 2 — Upper bound on s
There is no (115, 188, 472)-net in base 2, because
- 1 times m-reduction [i] would yield (115, 187, 472)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 199 260080 740953 432525 644258 691623 299554 166915 591610 816850 > 2187 [i]