MinT - Best Known (96, 96+18, s)-Nets in Base 2

Best Known (96, 96+18, s)-Nets in Base 2

(96, 96+18, 480)-Net over F₂ — Constructive and digital

Digital (96, 114, 480)-net over F₂, using

trace code for nets [i] based on digital (1, 19, 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]

(96, 96+18, 1375)-Net over F₂ — Digital

Digital (96, 114, 1375)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹¹⁴, 1375, F₂, 3, 18) (dual of [(1375, 3), 4011, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2¹¹⁴, 4125, F₂, 18) (dual of [4125, 4011, 19]-code), using
  - 1 times truncation [i] based on linear OA(2¹¹⁵, 4126, F₂, 19) (dual of [4126, 4011, 20]-code), using
    - constructionÂ X applied to C_e(18) âŠ‚ C_e(14) [i] based on
      1. linear OA(2¹⁰⁹, 4096, F₂, 19) (dual of [4096, 3987, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      2. linear OA(2⁸⁵, 4096, F₂, 15) (dual of [4096, 4011, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      3. linear OA(2⁶, 30, F₂, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
        discarding factors / shortening the dual code based on linear OA(2⁶, 32, F₂, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
        Reedâ€“Muller code RM(1,5) [i]
        caps in base bÂ =Â 2 [i]

(96, 96+18, 26951)-Net in Base 2 — Upper bound on s

There is no (96, 114, 26952)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 20770 185911 918072 787629 584719 622136 > 2¹¹⁴ [i]