MinT - Best Known (61−14, 61, s)-Nets in Base 2

Best Known (61−14, 61, s)-Nets in Base 2

(61−14, 61, 96)-Net over F₂ — Constructive and digital

Digital (47, 61, 96)-net over F₂, using

2¹ times duplication [i] based on digital (46, 60, 96)-net over F₂, using
- trace code for nets [i] based on digital (1, 15, 24)-net over F₁₆, using
  - net from sequence [i] based on digital (1, 23)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]

(61−14, 61, 155)-Net over F₂ — Digital

Digital (47, 61, 155)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(2⁶¹, 155, F₂, 14) (dual of [155, 94, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2⁶¹, 277, F₂, 14) (dual of [277, 216, 15]-code), using
  - 1 times truncation [i] based on linear OA(2⁶², 278, F₂, 15) (dual of [278, 216, 16]-code), using
    - extended or lengthened BCH codes [i]

(61−14, 61, 1409)-Net in Base 2 — Upper bound on s

There is no (47, 61, 1410)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 309520 154234 686848 > 2⁶¹ [i]