MinT - Best Known (18, 24, s)-Nets in Base 2

Best Known (18, 24, s)-Nets in Base 2

(18, 24, 130)-Net over F₂ — Constructive and digital

Digital (18, 24, 130)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²⁴, 130, F₂, 6, 6) (dual of [(130, 6), 756, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2²⁴, 130, F₂, 5, 6) (dual of [(130, 5), 626, 7]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2³, 3, F₂, 5, 3) (dual of [(3, 5), 12, 4]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(5;12,2) [i]
    2. linear OOA(2²¹, 127, F₂, 5, 6) (dual of [(127, 5), 614, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (15, 21, 127)-net over F₂, using
        linear code embedding found in a computer search [i]

(18, 24, 461)-Net in Base 2 — Upper bound on s

There is no (18, 24, 462)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 16 864310 > 2²⁴ [i]