MinT - Information on Result #547476

Information on Result #547476

There is no linear OA(4²⁵⁰, 315, F₄, 184) (dual of [315, 65, 185]-code), because residual code would yield OA(4⁶⁶, 130, S₄, 46), but

the linear programming bound shows that MÂ â‰¥ 85 500710 239918 056937 598457 546238 392168 496999 270901 024710 954318 080473 368710 373299 035832 808436 315964 953731 304608 355750 246645 022441 479767 081267 450183 031027 677468 264465 769878 050974 025606 636483 022255 677878 529900 169697 457203 686915 248577 285367 284829 664396 835130 033909 912133 782675 145453 687064 932415 368496 018005 950464 / 14792 016291 163716 498341 420200 257279 735349 377972 186639 808748 146615 449714 019754 184535 021829 772011 820648 802061 890427 812547 915746 041997 531764 615184 271242 411578 612781 720673 055112 499459 082243 654360 383640 447129 126316 017328 820016 161466 487961 088647 669558 103641 211639 601677 558307 > 4⁶⁶ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(4²⁵¹, 316, F₄, 185) (dual of [316, 65, 186]-code)	[i]	Truncation
2	No linear OA(4²⁵², 317, F₄, 186) (dual of [317, 65, 187]-code)	[i]
3	No linear OA(4²⁵³, 318, F₄, 187) (dual of [318, 65, 188]-code)	[i]
4	No linear OOA(4²⁵¹, 315, F₄, 2, 185) (dual of [(315, 2), 379, 186]-NRT-code)	[i]	m-Reduction for OOAs
5	No linear OOA(4²⁵², 315, F₄, 2, 186) (dual of [(315, 2), 378, 187]-NRT-code)	[i]
6	No linear OOA(4²⁵³, 315, F₄, 2, 187) (dual of [(315, 2), 377, 188]-NRT-code)	[i]
7	No linear OOA(4²⁵⁰, 315, F₄, 2, 184) (dual of [(315, 2), 380, 185]-NRT-code)	[i]	Depth Reduction
8	No linear OOA(4²⁵⁰, 315, F₄, 3, 184) (dual of [(315, 3), 695, 185]-NRT-code)	[i]	Depth Reduction
9	No digital (66, 250, 315)-net over F₄	[i]	Extracting Embedded Orthogonal Array