Best Known (61, 229, s)-Nets in Base 4
(61, 229, 66)-Net over F4 — Constructive and digital
Digital (61, 229, 66)-net over F4, using
- t-expansion [i] based on digital (49, 229, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
(61, 229, 99)-Net over F4 — Digital
Digital (61, 229, 99)-net over F4, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 61 and N(F) ≥ 99, using
(61, 229, 303)-Net over F4 — Upper bound on s (digital)
There is no digital (61, 229, 304)-net over F4, because
- extracting embedded orthogonal array [i] would yield linear OA(4229, 304, F4, 168) (dual of [304, 75, 169]-code), but
- residual code [i] would yield OA(461, 135, S4, 42), but
- the linear programming bound shows that M ≥ 14553 096315 947253 640884 776913 168926 302451 665455 919283 135527 723519 103281 609358 744533 636652 915559 579757 398043 602406 873493 852833 510337 625815 402107 895808 / 2665 663747 457635 051830 020094 359849 599949 322414 129592 914794 116842 536378 425306 982781 909625 123448 656307 846295 612863 > 461 [i]
- residual code [i] would yield OA(461, 135, S4, 42), but
(61, 229, 402)-Net in Base 4 — Upper bound on s
There is no (61, 229, 403)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 840711 346575 487982 329616 852066 436810 933640 778071 235465 464716 114352 129699 419501 745055 542665 653619 022184 390536 304394 983829 612608 723709 222112 > 4229 [i]