Best Known (36−30, 36, s)-Nets in Base 7
(36−30, 36, 14)-Net over F7 — Constructive and digital
Digital (6, 36, 14)-net over F7, using
- net from sequence [i] based on digital (6, 13)-sequence over F7, using
(36−30, 36, 24)-Net over F7 — Digital
Digital (6, 36, 24)-net over F7, using
- t-expansion [i] based on digital (4, 36, 24)-net over F7, using
- net from sequence [i] based on digital (4, 23)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 4 and N(F) ≥ 24, using
- net from sequence [i] based on digital (4, 23)-sequence over F7, using
(36−30, 36, 93)-Net over F7 — Upper bound on s (digital)
There is no digital (6, 36, 94)-net over F7, because
- extracting embedded orthogonal array [i] would yield linear OA(736, 94, F7, 30) (dual of [94, 58, 31]-code), but
- construction Y1 [i] would yield
- linear OA(735, 45, F7, 30) (dual of [45, 10, 31]-code), but
- construction Y1 [i] would yield
- linear OA(734, 37, F7, 30) (dual of [37, 3, 31]-code), but
- “Hi4†bound on codes from Brouwer’s database [i]
- linear OA(710, 45, F7, 8) (dual of [45, 35, 9]-code), but
- discarding factors / shortening the dual code would yield linear OA(710, 42, F7, 8) (dual of [42, 32, 9]-code), but
- construction Y1 [i] would yield
- linear OA(79, 14, F7, 8) (dual of [14, 5, 9]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- linear OA(732, 42, F7, 28) (dual of [42, 10, 29]-code), but
- discarding factors / shortening the dual code would yield linear OA(732, 38, F7, 28) (dual of [38, 6, 29]-code), but
- linear OA(79, 14, F7, 8) (dual of [14, 5, 9]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(710, 42, F7, 8) (dual of [42, 32, 9]-code), but
- linear OA(734, 37, F7, 30) (dual of [37, 3, 31]-code), but
- construction Y1 [i] would yield
- OA(758, 94, S7, 49), but
- the linear programming bound shows that M ≥ 10580 743749 861231 293497 451788 690805 914704 925957 518061 849209 488293 043893 822152 954067 592535 777967 / 972 197243 784671 062972 315640 073851 274697 000575 > 758 [i]
- linear OA(735, 45, F7, 30) (dual of [45, 10, 31]-code), but
- construction Y1 [i] would yield
(36−30, 36, 94)-Net in Base 7 — Upper bound on s
There is no (6, 36, 95)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(736, 95, S7, 30), but
- the linear programming bound shows that M ≥ 496534 530419 888355 667526 145518 013316 218272 013330 824014 844687 719000 / 168819 808572 723031 224841 890170 628547 > 736 [i]