Best Known (97−96, 97, s)-Nets in Base 27
(97−96, 97, 38)-Net over F27 — Constructive and digital
Digital (1, 97, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
(97−96, 97, 55)-Net over F27 — Upper bound on s (digital)
There is no digital (1, 97, 56)-net over F27, because
- 44 times m-reduction [i] would yield digital (1, 53, 56)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(2753, 56, F27, 52) (dual of [56, 3, 53]-code), but
(97−96, 97, 56)-Net in Base 27 — Upper bound on s
There is no (1, 97, 57)-net in base 27, because
- 42 times m-reduction [i] would yield (1, 55, 57)-net in base 27, but
- extracting embedded orthogonal array [i] would yield OA(2755, 57, S27, 54), but
- the (dual) Plotkin bound shows that M ≥ 430 023359 390034 222082 732011 948356 798311 147247 214997 695270 038813 781532 497547 421283 / 55 > 2755 [i]
- extracting embedded orthogonal array [i] would yield OA(2755, 57, S27, 54), but