Best Known (27, 63, s)-Nets in Base 256
(27, 63, 523)-Net over F256 — Constructive and digital
Digital (27, 63, 523)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (4, 22, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- digital (5, 41, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- digital (4, 22, 261)-net over F256, using
(27, 63, 1198)-Net over F256 — Digital
Digital (27, 63, 1198)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25663, 1198, F256, 36) (dual of [1198, 1135, 37]-code), using
- 170 step Varšamov–Edel lengthening with (ri) = (2, 29 times 0, 1, 139 times 0) [i] based on linear OA(25660, 1025, F256, 36) (dual of [1025, 965, 37]-code), using
- extended algebraic-geometric code AGe(F,988P) [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025, using
- K1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- extended algebraic-geometric code AGe(F,988P) [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025, using
- 170 step Varšamov–Edel lengthening with (ri) = (2, 29 times 0, 1, 139 times 0) [i] based on linear OA(25660, 1025, F256, 36) (dual of [1025, 965, 37]-code), using
(27, 63, 7951137)-Net in Base 256 — Upper bound on s
There is no (27, 63, 7951138)-net in base 256, because
- the generalized Rao bound for nets shows that 256m ≥ 52 374259 344699 206215 199558 983191 353755 476711 703594 805537 028380 545653 107232 966039 151083 487369 710242 031433 859701 410316 989941 790361 255290 655421 915656 776496 > 25663 [i]