Best Known (63−28, 63, s)-Nets in Base 27
(63−28, 63, 192)-Net over F27 — Constructive and digital
Digital (35, 63, 192)-net over F27, using
- 1 times m-reduction [i] based on digital (35, 64, 192)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 13, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (4, 18, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 33, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 13, 64)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(63−28, 63, 370)-Net in Base 27 — Constructive
(35, 63, 370)-net in base 27, using
- 13 times m-reduction [i] based on (35, 76, 370)-net in base 27, using
- base change [i] based on digital (16, 57, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 57, 370)-net over F81, using
(63−28, 63, 937)-Net over F27 — Digital
Digital (35, 63, 937)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2763, 937, F27, 28) (dual of [937, 874, 29]-code), using
- 198 step Varšamov–Edel lengthening with (ri) = (4, 1, 0, 1, 4 times 0, 1, 13 times 0, 1, 29 times 0, 1, 55 times 0, 1, 89 times 0) [i] based on linear OA(2753, 729, F27, 28) (dual of [729, 676, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 198 step Varšamov–Edel lengthening with (ri) = (4, 1, 0, 1, 4 times 0, 1, 13 times 0, 1, 29 times 0, 1, 55 times 0, 1, 89 times 0) [i] based on linear OA(2753, 729, F27, 28) (dual of [729, 676, 29]-code), using
(63−28, 63, 642120)-Net in Base 27 — Upper bound on s
There is no (35, 63, 642121)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1 499413 414616 829789 510816 313750 201600 975890 460736 163648 330064 342994 712412 758332 043150 659961 > 2763 [i]