MinT - Best Known (36, 74, s)-Nets in Base 81

Best Known (36, 74, s)-Nets in Base 81

Digital (36, 74, 730)-net over F₈₁, using

net from sequence [i] based on digital (36, 729)-sequence over F₈₁, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 36 and N(F) ≥ 730, using
  - the Hermitian function field over F₈₁ [i]

Digital (36, 74, 1307)-net over F₈₁, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(81⁷⁴, 1307, F₈₁, 38) (dual of [1307, 1233, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(81⁷⁴, 1313, F₈₁, 38) (dual of [1313, 1239, 39]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(81⁷³, 1312, F₈₁, 38) (dual of [1312, 1239, 39]-code), using
    - the BCH-code C(I) with length 1312Â | 81²âˆ’1, defining interval IÂ =Â {1,40,79,…,132}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]

There is no (36, 74, 2686402)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 1690 022730 894282 705574 525293 977717 052409 078999 454310 867993 563330 805702 118647 883071 324483 625679 373911 729066 798324 632740 659622 769618 298115 926241 > 81⁷⁴ [i]