Best Known (60, 60+33, s)-Nets in Base 27
(60, 60+33, 615)-Net over F27 — Constructive and digital
Digital (60, 93, 615)-net over F27, using
- net defined by OOA [i] based on linear OOA(2793, 615, F27, 33, 33) (dual of [(615, 33), 20202, 34]-NRT-code), using
(60, 60+33, 730)-Net in Base 27 — Constructive
(60, 93, 730)-net in base 27, using
- 3 times m-reduction [i] based on (60, 96, 730)-net in base 27, using
- base change [i] based on digital (36, 72, 730)-net over F81, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- the Hermitian function field over F81 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
- base change [i] based on digital (36, 72, 730)-net over F81, using
(60, 60+33, 8437)-Net over F27 — Digital
Digital (60, 93, 8437)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2793, 8437, F27, 33) (dual of [8437, 8344, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2793, 9841, F27, 33) (dual of [9841, 9748, 34]-code), using
(60, 60+33, large)-Net in Base 27 — Upper bound on s
There is no (60, 93, large)-net in base 27, because
- 31 times m-reduction [i] would yield (60, 62, large)-net in base 27, but