Best Known (10, 41, s)-Nets in Base 4
(10, 41, 27)-Net over F4 — Constructive and digital
Digital (10, 41, 27)-net over F4, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 10 and N(F) ≥ 27, using
(10, 41, 50)-Net over F4 — Upper bound on s (digital)
There is no digital (10, 41, 51)-net over F4, because
- extracting embedded orthogonal array [i] would yield linear OA(441, 51, F4, 31) (dual of [51, 10, 32]-code), but
- “Gur†bound on codes from Brouwer’s database [i]
(10, 41, 52)-Net in Base 4 — Upper bound on s
There is no (10, 41, 53)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(441, 53, S4, 31), but
- the linear programming bound shows that M ≥ 1279 874020 176133 246331 057157 963776 / 218 103641 > 441 [i]