Best Known (77−34, 77, s)-Nets in Base 32
(77−34, 77, 240)-Net over F32 — Constructive and digital
Digital (43, 77, 240)-net over F32, using
- 8 times m-reduction [i] based on digital (43, 85, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 32, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- digital (11, 53, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 32, 120)-net over F32, using
- (u, u+v)-construction [i] based on
(77−34, 77, 513)-Net in Base 32 — Constructive
(43, 77, 513)-net in base 32, using
- 13 times m-reduction [i] based on (43, 90, 513)-net in base 32, using
- base change [i] based on digital (28, 75, 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, 75, 513)-net over F64, using
(77−34, 77, 1399)-Net over F32 — Digital
Digital (43, 77, 1399)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3277, 1399, F32, 34) (dual of [1399, 1322, 35]-code), using
- 361 step Varšamov–Edel lengthening with (ri) = (6, 0, 1, 0, 0, 0, 1, 9 times 0, 1, 18 times 0, 1, 35 times 0, 1, 63 times 0, 1, 97 times 0, 1, 127 times 0) [i] based on linear OA(3264, 1025, F32, 34) (dual of [1025, 961, 35]-code), using
(77−34, 77, 1520635)-Net in Base 32 — Upper bound on s
There is no (43, 77, 1520636)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 78 804558 132894 957076 894228 351993 379002 401645 070530 082765 263328 882417 280644 683950 766818 417514 101407 191255 519382 123297 > 3277 [i]