MinT - Best Known (120, 120+21, s)-Nets in Base 8

Best Known (120, 120+21, s)-Nets in Base 8

(120, 120+21, 209740)-Net over F₈ — Constructive and digital

Digital (120, 141, 209740)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (4, 14, 25)-net over F₈, using
  - net from sequence [i] based on digital (4, 24)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
      - a function field by SÃ©mirat [i]
2. digital (106, 127, 209715)-net over F₈, using
  - net defined by OOA [i] based on linear OOA(8¹²⁷, 209715, F₈, 21, 21) (dual of [(209715, 21), 4403888, 22]-NRT-code), using
    - OOA 10-folding and stacking with additional row [i] based on linear OA(8¹²⁷, 2097151, F₈, 21) (dual of [2097151, 2097024, 22]-code), using
      - discarding factors / shortening the dual code based on linear OA(8¹²⁷, 2097152, F₈, 21) (dual of [2097152, 2097025, 22]-code), using
        an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

(120, 120+21, 2760541)-Net over F₈ — Digital

Digital (120, 141, 2760541)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 120+21, large)-Net in Base 8 — Upper bound on s

There is no (120, 141, large)-net in base 8, because

19 times m-reduction [i] would yield (120, 122, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]