Best Known (6, 6+42, s)-Nets in Base 8
(6, 6+42, 28)-Net over F8 — Constructive and digital
Digital (6, 48, 28)-net over F8, using
- t-expansion [i] based on digital (5, 48, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
(6, 6+42, 33)-Net over F8 — Digital
Digital (6, 48, 33)-net over F8, using
- net from sequence [i] based on digital (6, 32)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 6 and N(F) ≥ 33, using
(6, 6+42, 57)-Net over F8 — Upper bound on s (digital)
There is no digital (6, 48, 58)-net over F8, because
- extracting embedded orthogonal array [i] would yield linear OA(848, 58, F8, 42) (dual of [58, 10, 43]-code), but
- construction Y1 [i] would yield
- linear OA(847, 50, F8, 42) (dual of [50, 3, 43]-code), but
- “Hi4†bound on codes from Brouwer’s database [i]
- OA(810, 58, S8, 8), but
- discarding factors would yield OA(810, 57, S8, 8), but
- the linear programming bound shows that M ≥ 1426 626655 027200 / 1 315507 > 810 [i]
- discarding factors would yield OA(810, 57, S8, 8), but
- linear OA(847, 50, F8, 42) (dual of [50, 3, 43]-code), but
- construction Y1 [i] would yield
(6, 6+42, 78)-Net in Base 8 — Upper bound on s
There is no (6, 48, 79)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(848, 79, S8, 42), but
- the linear programming bound shows that M ≥ 61211 439540 208648 467887 923180 473724 818344 478050 565448 173057 950881 939456 / 2623 138072 234251 925767 876605 > 848 [i]