MinT - Best Known (31, 31+12, s)-Nets in Base 4

Best Known (31, 31+12, s)-Nets in Base 4

Digital (31, 43, 240)-net over F₄, using

2 times m-reduction [i] based on digital (31, 45, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 15, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

Digital (31, 43, 377)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4⁴³, 377, F₄, 12) (dual of [377, 334, 13]-code), using
- 115 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (2, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 21 times 0, 1, 30 times 0, 1, 38 times 0) [i] based on linear OA(4³⁶, 255, F₄, 12) (dual of [255, 219, 13]-code), using
  - the primitive narrow-sense BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

(31, 43, 387)-net in base 4, using

There is no (31, 43, 20596)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 77 385848 754068 248962 302884 > 4⁴³ [i]