Best Known (29, 29+36, s)-Nets in Base 64
(29, 29+36, 513)-Net over F64 — Constructive and digital
Digital (29, 65, 513)-net over F64, using
- t-expansion [i] based on digital (28, 65, 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
(29, 29+36, 525)-Net over F64 — Digital
Digital (29, 65, 525)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6465, 525, F64, 36) (dual of [525, 460, 37]-code), using
- 11 step Varšamov–Edel lengthening with (ri) = (1, 10 times 0) [i] based on linear OA(6464, 513, F64, 36) (dual of [513, 449, 37]-code), using
- extended algebraic-geometric code AGe(F,476P) [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- extended algebraic-geometric code AGe(F,476P) [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- 11 step Varšamov–Edel lengthening with (ri) = (1, 10 times 0) [i] based on linear OA(6464, 513, F64, 36) (dual of [513, 449, 37]-code), using
(29, 29+36, 399113)-Net in Base 64 — Upper bound on s
There is no (29, 65, 399114)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 2521 774609 085566 533227 890246 813810 030303 749653 641165 305030 123086 932426 386189 870217 463529 506368 392064 814893 619497 956160 > 6465 [i]