Best Known (48−39, 48, s)-Nets in Base 5
(48−39, 48, 26)-Net over F5 — Constructive and digital
Digital (9, 48, 26)-net over F5, using
- net from sequence [i] based on digital (9, 25)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 9 and N(F) ≥ 26, using
(48−39, 48, 53)-Net over F5 — Upper bound on s (digital)
There is no digital (9, 48, 54)-net over F5, because
- extracting embedded orthogonal array [i] would yield linear OA(548, 54, F5, 39) (dual of [54, 6, 40]-code), but
- “DG1†bound on codes from Brouwer’s database [i]
(48−39, 48, 55)-Net in Base 5 — Upper bound on s
There is no (9, 48, 56)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(548, 56, S5, 39), but
- the linear programming bound shows that M ≥ 877520 278663 723729 550838 470458 984375 / 207 > 548 [i]