MinT - Best Known (43, 77, s)-Nets in Base 32

Best Known (43, 77, s)-Nets in Base 32

Digital (43, 77, 240)-net over F₃₂, using

(43, 77, 513)-net in base 32, using

13 times m-reduction [i] based on (43, 90, 513)-net in base 32, using
- base change [i] based on digital (28, 75, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

Digital (43, 77, 1399)-net over F₃₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(32⁷⁷, 1399, F₃₂, 34) (dual of [1399, 1322, 35]-code), using
- 361 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (6, 0, 1, 0, 0, 0, 1, 9 times 0, 1, 18 times 0, 1, 35 times 0, 1, 63 times 0, 1, 97 times 0, 1, 127 times 0) [i] based on linear OA(32⁶⁴, 1025, F₃₂, 34) (dual of [1025, 961, 35]-code), using
  - the BCH-code C(I) with length 1025Â | 32⁴âˆ’1, defining interval IÂ =Â {1,32,63,…,1024}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]

There is no (43, 77, 1520636)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 78 804558 132894 957076 894228 351993 379002 401645 070530 082765 263328 882417 280644 683950 766818 417514 101407 191255 519382 123297 > 32⁷⁷ [i]