Best Known (97, 97+41, s)-Nets in Base 8
(97, 97+41, 1026)-Net over F8 — Constructive and digital
Digital (97, 138, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 69, 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
(97, 97+41, 2960)-Net over F8 — Digital
Digital (97, 138, 2960)-net over F8, using
(97, 97+41, 1821258)-Net in Base 8 — Upper bound on s
There is no (97, 138, 1821259)-net in base 8, because
- 1 times m-reduction [i] would yield (97, 137, 1821259)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 5288 461347 896997 294805 959208 130044 059505 817520 258131 157008 336917 686415 569545 934492 273847 220211 409554 790275 115063 530352 605112 > 8137 [i]