Best Known (111, 162, s)-Nets in Base 8
(111, 162, 1026)-Net over F8 — Constructive and digital
Digital (111, 162, 1026)-net over F8, using
- 4 times m-reduction [i] based on digital (111, 166, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 83, 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
- trace code for nets [i] based on digital (28, 83, 513)-net over F64, using
(111, 162, 2372)-Net over F8 — Digital
Digital (111, 162, 2372)-net over F8, using
(111, 162, 951524)-Net in Base 8 — Upper bound on s
There is no (111, 162, 951525)-net in base 8, because
- 1 times m-reduction [i] would yield (111, 161, 951525)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 24 973998 320904 492343 790501 071351 602483 103194 936294 541269 770339 961563 777264 387079 516939 437826 453592 291489 802324 851352 480132 664574 750934 942693 144528 > 8161 [i]