Best Known (43−25, 43, s)-Nets in Base 64
(43−25, 43, 208)-Net over F64 — Constructive and digital
Digital (18, 43, 208)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (3, 15, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- digital (3, 28, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64 (see above)
- digital (3, 15, 104)-net over F64, using
(43−25, 43, 288)-Net in Base 64 — Constructive
(18, 43, 288)-net in base 64, using
- 20 times m-reduction [i] based on (18, 63, 288)-net in base 64, using
- base change [i] based on digital (9, 54, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 54, 288)-net over F128, using
(43−25, 43, 288)-Net over F64 — Digital
Digital (18, 43, 288)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6443, 288, F64, 25) (dual of [288, 245, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(6443, 293, F64, 25) (dual of [293, 250, 26]-code), using
- 30 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 6 times 0, 1, 19 times 0) [i] based on linear OA(6437, 257, F64, 25) (dual of [257, 220, 26]-code), using
- extended algebraic-geometric code AGe(F,231P) [i] based on function field F/F64 with g(F) = 12 and N(F) ≥ 257, using
- 30 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 6 times 0, 1, 19 times 0) [i] based on linear OA(6437, 257, F64, 25) (dual of [257, 220, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(6443, 293, F64, 25) (dual of [293, 250, 26]-code), using
(43−25, 43, 321)-Net in Base 64
(18, 43, 321)-net in base 64, using
- 21 times m-reduction [i] based on (18, 64, 321)-net in base 64, using
- base change [i] based on digital (2, 48, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 48, 321)-net over F256, using
(43−25, 43, 176050)-Net in Base 64 — Upper bound on s
There is no (18, 43, 176051)-net in base 64, because
- 1 times m-reduction [i] would yield (18, 42, 176051)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 7237 357614 248000 445977 419079 973477 152705 827202 492868 599363 041387 900087 488316 > 6442 [i]