Best Known (97−43, 97, s)-Nets in Base 32
(97−43, 97, 272)-Net over F32 — Constructive and digital
Digital (54, 97, 272)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (5, 19, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- digital (7, 28, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (7, 50, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (5, 19, 76)-net over F32, using
(97−43, 97, 513)-Net in Base 32 — Constructive
(54, 97, 513)-net in base 32, using
- t-expansion [i] based on (46, 97, 513)-net in base 32, using
- 11 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- 11 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
(97−43, 97, 1616)-Net over F32 — Digital
Digital (54, 97, 1616)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3297, 1616, F32, 43) (dual of [1616, 1519, 44]-code), using
- 1518 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 17 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 25 times 0, 1, 26 times 0, 1, 29 times 0, 1, 32 times 0, 1, 35 times 0, 1, 37 times 0, 1, 42 times 0, 1, 44 times 0, 1, 49 times 0, 1, 54 times 0, 1, 58 times 0, 1, 63 times 0, 1, 69 times 0, 1, 75 times 0, 1, 82 times 0, 1, 88 times 0, 1, 97 times 0, 1, 105 times 0, 1, 114 times 0, 1, 125 times 0) [i] based on linear OA(3243, 44, F32, 43) (dual of [44, 1, 44]-code or 44-arc in PG(42,32)), using
- dual of repetition code with length 44 [i]
- 1518 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 11 times 0, 1, 11 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 17 times 0, 1, 19 times 0, 1, 20 times 0, 1, 22 times 0, 1, 25 times 0, 1, 26 times 0, 1, 29 times 0, 1, 32 times 0, 1, 35 times 0, 1, 37 times 0, 1, 42 times 0, 1, 44 times 0, 1, 49 times 0, 1, 54 times 0, 1, 58 times 0, 1, 63 times 0, 1, 69 times 0, 1, 75 times 0, 1, 82 times 0, 1, 88 times 0, 1, 97 times 0, 1, 105 times 0, 1, 114 times 0, 1, 125 times 0) [i] based on linear OA(3243, 44, F32, 43) (dual of [44, 1, 44]-code or 44-arc in PG(42,32)), using
(97−43, 97, 2127229)-Net in Base 32 — Upper bound on s
There is no (54, 97, 2127230)-net in base 32, because
- 1 times m-reduction [i] would yield (54, 96, 2127230)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 3 121769 756360 524505 838718 428163 151841 157558 439038 108516 254784 621318 057061 418015 399927 613424 495142 624720 715773 444118 180865 141108 271790 638388 425781 > 3296 [i]