Best Known (46−31, 46, s)-Nets in Base 3
(46−31, 46, 28)-Net over F3 — Constructive and digital
Digital (15, 46, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
(46−31, 46, 54)-Net over F3 — Upper bound on s (digital)
There is no digital (15, 46, 55)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(346, 55, F3, 31) (dual of [55, 9, 32]-code), but
- “Gur†bound on codes from Brouwer’s database [i]
(46−31, 46, 56)-Net in Base 3 — Upper bound on s
There is no (15, 46, 57)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(346, 57, S3, 31), but
- the linear programming bound shows that M ≥ 109 838392 116853 446081 848097 / 11440 > 346 [i]