Best Known (104−46, 104, s)-Nets in Base 27
(104−46, 104, 240)-Net over F27 — Constructive and digital
Digital (58, 104, 240)-net over F27, using
- 1 times m-reduction [i] based on digital (58, 105, 240)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 21, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (7, 30, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (7, 54, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27 (see above)
- digital (6, 21, 76)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(104−46, 104, 370)-Net in Base 27 — Constructive
(58, 104, 370)-net in base 27, using
- t-expansion [i] based on (43, 104, 370)-net in base 27, using
- 4 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 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, 81, 370)-net over F81, using
- 4 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(104−46, 104, 1401)-Net over F27 — Digital
Digital (58, 104, 1401)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(27104, 1401, F27, 46) (dual of [1401, 1297, 47]-code), using
- 1296 step Varšamov–Edel lengthening with (ri) = (3, 2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 29 times 0, 1, 30 times 0, 1, 33 times 0, 1, 35 times 0, 1, 39 times 0, 1, 41 times 0, 1, 45 times 0, 1, 48 times 0, 1, 53 times 0, 1, 56 times 0, 1, 61 times 0, 1, 65 times 0, 1, 71 times 0, 1, 76 times 0, 1, 82 times 0, 1, 88 times 0, 1, 96 times 0) [i] based on linear OA(2746, 47, F27, 46) (dual of [47, 1, 47]-code or 47-arc in PG(45,27)), using
- dual of repetition code with length 47 [i]
- 1296 step Varšamov–Edel lengthening with (ri) = (3, 2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0, 1, 14 times 0, 1, 14 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 29 times 0, 1, 30 times 0, 1, 33 times 0, 1, 35 times 0, 1, 39 times 0, 1, 41 times 0, 1, 45 times 0, 1, 48 times 0, 1, 53 times 0, 1, 56 times 0, 1, 61 times 0, 1, 65 times 0, 1, 71 times 0, 1, 76 times 0, 1, 82 times 0, 1, 88 times 0, 1, 96 times 0) [i] based on linear OA(2746, 47, F27, 46) (dual of [47, 1, 47]-code or 47-arc in PG(45,27)), using
(104−46, 104, 1075800)-Net in Base 27 — Upper bound on s
There is no (58, 104, 1075801)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 72750 775300 748599 585464 024067 638702 955733 312955 457985 237095 285251 153628 158844 416625 753530 831307 310247 696893 862995 017741 791724 034319 025596 677297 306643 > 27104 [i]