Best Known (88, 88+32, s)-Nets in Base 8
(88, 88+32, 1026)-Net over F8 — Constructive and digital
Digital (88, 120, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 60, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(88, 88+32, 5571)-Net over F8 — Digital
Digital (88, 120, 5571)-net over F8, using
(88, 88+32, 5762551)-Net in Base 8 — Upper bound on s
There is no (88, 120, 5762552)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 2 348543 262460 947743 052928 806735 013201 535535 241199 792001 247007 034507 688117 225563 246364 762189 112231 142250 166415 > 8120 [i]