Best Known (22, 54, s)-Nets in Base 256
(22, 54, 520)-Net over F256 — Constructive and digital
Digital (22, 54, 520)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (3, 19, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- digital (3, 35, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256 (see above)
- digital (3, 19, 260)-net over F256, using
(22, 54, 793)-Net over F256 — Digital
Digital (22, 54, 793)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25654, 793, F256, 32) (dual of [793, 739, 33]-code), using
- 19 step Varšamov–Edel lengthening with (ri) = (1, 18 times 0) [i] based on linear OA(25653, 773, F256, 32) (dual of [773, 720, 33]-code), using
- construction X applied to C([241,272]) ⊂ C([242,272]) [i] based on
- linear OA(25653, 771, F256, 32) (dual of [771, 718, 33]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {241,242,…,272}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(25651, 771, F256, 31) (dual of [771, 720, 32]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {242,243,…,272}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to C([241,272]) ⊂ C([242,272]) [i] based on
- 19 step Varšamov–Edel lengthening with (ri) = (1, 18 times 0) [i] based on linear OA(25653, 773, F256, 32) (dual of [773, 720, 33]-code), using
(22, 54, 3579377)-Net in Base 256 — Upper bound on s
There is no (22, 54, 3579378)-net in base 256, because
- the generalized Rao bound for nets shows that 256m ≥ 11090 701230 702356 181388 957571 593150 034011 794845 986075 577910 583580 814050 773226 876548 085683 030519 526783 567668 162648 181647 170679 061491 > 25654 [i]