Best Known (63−45, 63, s)-Nets in Base 27
(63−45, 63, 108)-Net over F27 — Constructive and digital
Digital (18, 63, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
(63−45, 63, 116)-Net in Base 27 — Constructive
(18, 63, 116)-net in base 27, using
- 1 times m-reduction [i] based on (18, 64, 116)-net in base 27, using
- base change [i] based on digital (2, 48, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 48, 116)-net over F81, using
(63−45, 63, 148)-Net over F27 — Digital
Digital (18, 63, 148)-net over F27, using
- net from sequence [i] based on digital (18, 147)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 148, using
(63−45, 63, 3753)-Net in Base 27 — Upper bound on s
There is no (18, 63, 3754)-net in base 27, because
- 1 times m-reduction [i] would yield (18, 62, 3754)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 55761 604822 450455 131111 511322 144171 719387 450695 063150 388344 813450 658182 846139 780025 310349 > 2762 [i]